JP4456029B2 - 3D information restoration device for rotating body - Google Patents

Description

  The present invention relates to a three-dimensional information restoration apparatus for a rotating body, and in particular, based on a single two-dimensional image obtained by photographing an object made of a rotating body such as pottery from a predetermined direction. The present invention relates to a technique for restoring three-dimensional information.

  Due to the improvement in computer performance, methods for handling an object as a three-dimensional image have already been generalized, and three-dimensional image data is used in various fields of the industry including the CG field. However, the three-dimensional image is an image defined in the virtual space inside the computer to the last, and is handled as a two-dimensional image on the printed matter and the display screen used in the real society. Therefore, even if 3D image data is prepared inside the computer, it is generally converted to 2D image data and finally output.

  In addition, when a photograph of a three-dimensional object is taken by a normal method, only information as a two-dimensional image is recorded on the photograph. Therefore, an object expressed as a two-dimensional image is printed on a printed matter that we regularly obtain.

Under such circumstances, a technique for restoring original three-dimensional image information based on two-dimensional image data of an object has been proposed. For example, Patent Documents 1 and 2 listed below disclose techniques for generating a virtual three-dimensional image of an object based on a plurality of two-dimensional images obtained by photographing the same object from different directions. Patent Document 3 below discloses a technique for estimating the inclination of a minute area on the surface of an original object by restoring the frequency component of the surface texture of the object image on the two-dimensional image and restoring the three-dimensional shape. Is disclosed.
JP 2002-016945 A Japanese Patent Laid-Open No. 2003-331262 JP-A-5-264244

  As described above, several techniques have already been known for restoring the original three-dimensional image information based on the two-dimensional image data of the object. However, many of these are methods that require a plurality of two-dimensional images obtained by photographing the same object under different photographing conditions, and cannot be restored based on a single two-dimensional image. For this reason, the method disclosed in the above-mentioned patent document should be applied to a use in which the three-dimensional information of the original object is restored based on a single photograph published in a printed matter such as a magazine or a catalog. I can't.

  Of course, several methods have been proposed to restore the original 3D information based on a single 2D image. However, there are many manual processes by skilled workers, which are practical on a commercial basis. It has not reached a practical method.

  Accordingly, an object of the present invention is to provide an apparatus that can restore three-dimensional information of an object using only one two-dimensional image of the object and with a relatively easy work load.

(1) The first aspect of the present invention is a third-order rotator that restores three-dimensional information of an original object based on a two-dimensional image obtained by photographing an object made of the rotator from a predetermined direction. In the original information restoration device,
Two-dimensional image input means for inputting a two-dimensional image including an object image obtained by photographing an object made of a rotating body under predetermined photographing conditions;
Photographing condition input means for inputting information indicating “distance f between viewpoint and projection plane” given as one of photographing conditions;
Based on the position and shape of the two sets of arc-shaped features included in the input object image on the two-dimensional image and the distance f between the viewpoint and the projection plane, the optical axis L that is one of the imaging conditions Projection conditions for determining a position and determining, as projection conditions, a predetermined projection plane S orthogonal to the optical axis L and a viewpoint E located at a distance f from the projection plane S along the optical axis L A determination means;
With the input two-dimensional image arranged on the projection surface S so that the center point of the input two-dimensional image coincides with the foot G of the perpendicular line drawn from the viewpoint E to the projection surface S, the one side surface of the object image is displayed. Contour extracting means for extracting the contour CCside;
Based on the information indicating the positions of the projection plane S, the viewpoint E, and the contour line CCside in the three-dimensional coordinate system, by performing perspective projection on the projection plane S with the viewpoint E as a reference, the tertiary of the object that can obtain the contour line CCside Three-dimensional information creating means for creating original information by considering the condition that the object is a rotating body;
Is provided.

(2) According to a second aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first aspect described above,
Projection condition determination means
In the XYZ three-dimensional coordinate system, a parameter that defines the position of the optical axis L, a parameter that defines a first reference circle that is included in a first plane orthogonal to the Z axis and that has a center point on the Z axis, and Z A parameter setting unit that sets a parameter that defines a second reference circle that is included in a second plane orthogonal to the axis and that has a center point on the Z axis, based on an instruction from the operator;
On the XYZ three-dimensional coordinate system, a predetermined projection plane S orthogonal to the optical axis L and a viewpoint E located at a distance f from the projection plane S along the optical axis L are defined. A perspective projection computing unit that perspectively projects the reference circle of 1 and the second reference circle onto the projection plane S with the viewpoint E as a reference, and obtains a first circle projection image and a second circle projection image on the projection plane S; ,
The two-dimensional image is arranged on the projection plane S so that the center point of the input two-dimensional image coincides with the foot G of the perpendicular line drawn from the viewpoint E to the projection plane S, and the first two-dimensional image is displayed on the two-dimensional image. A superimposed display unit that displays a superimposed state of the circle projection image and the second circle projection image on the display screen;
In the display by the superimposed display unit, the first arc-shaped feature of the object image and the whole or a part of the first circular projection image coincide with each other with a predetermined accuracy, and the second arc-shaped feature of the object image and the second arc-shaped feature The projection plane S and the viewpoint E defined by the perspective projection calculation unit are projected as projection conditions when a coincidence confirmation indicating that all or a part of the circle projection image of the circle coincides with a predetermined accuracy is obtained. A condition determining unit that determines the surface S and the viewpoint E;
It is constituted by.

(3) According to a third aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first aspect described above,
Three-dimensional information creation means
A reference point defining unit for defining a plurality of n reference points PP at predetermined intervals on the contour line CCside extracted by the contour line extracting means;
Corresponding points P corresponding to the respective reference points PP are defined as “a structural circle C included in a predetermined plane orthogonal to the Z axis on the XYZ three-dimensional coordinate system, having a center point on the Z axis, and passing through the corresponding point P. A two-dimensional vector TT obtained on the projection plane S is obtained by obtaining a tangent vector T at the corresponding point P with respect to the structural circle C, and perspectively projecting the tangent vector T onto the projection plane S with the viewpoint E as a reference. , A tangent of the contour line CCside at the reference point PP ”, a structural circle definition part that defines a plurality of n structural circles C,
Based on the set of structural circles C, a surface data creation unit that creates surface data of an object made of a rotating body and outputs this as 3D information;
It is constituted by.

(4) According to a fourth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first aspect described above,
Projection condition determination means
In the XYZ three-dimensional coordinate system, a parameter that defines the position of the optical axis L, a parameter that defines a first reference circle that is included in a first plane orthogonal to the Z axis and that has a center point on the Z axis, and Z A parameter setting unit that sets a parameter that defines a second reference circle that is included in a second plane orthogonal to the axis and that has a center point on the Z axis, based on an instruction from the operator;
On the XYZ three-dimensional coordinate system, a predetermined projection plane S orthogonal to the optical axis L and a viewpoint E located at a distance f from the projection plane S along the optical axis L are defined. A perspective projection computing unit that perspectively projects the reference circle of 1 and the second reference circle onto the projection plane S with the viewpoint E as a reference, and obtains a first circle projection image and a second circle projection image on the projection plane S; ,
The two-dimensional image is arranged on the projection plane S so that the center point of the input two-dimensional image coincides with the foot G of the perpendicular line drawn from the viewpoint E to the projection plane S, and the first two-dimensional image is displayed on the two-dimensional image. A superimposed display unit that displays a superimposed state of the circle projection image and the second circle projection image on the display screen;
In the display by the superimposed display unit, the first arc-shaped feature of the object image and the whole or a part of the first circular projection image coincide with each other with a predetermined accuracy, and the second arc-shaped feature of the object image and the second arc-shaped feature The projection plane S and the viewpoint E defined by the perspective projection calculation unit are projected as projection conditions when a coincidence confirmation indicating that all or a part of the circle projection image of the circle coincides with a predetermined accuracy is obtained. A condition determining unit that determines the surface S and the viewpoint E;
Composed by
Three-dimensional information creation means
A reference point defining unit for defining a plurality of n reference points PP at predetermined intervals on the contour line CCside extracted by the contour line extracting means;
Corresponding points P corresponding to the respective reference points PP are defined as “a structural circle C included in a predetermined plane orthogonal to the Z axis on the XYZ three-dimensional coordinate system, having a center point on the Z axis, and passing through the corresponding point P. A two-dimensional vector TT obtained on the projection plane S is obtained by obtaining a tangent vector T at the corresponding point P with respect to the structural circle C, and perspectively projecting the tangent vector T onto the projection plane S with the viewpoint E as a reference. , A tangent to the contour line CCside at the reference point PP ”, a structural circle definition part that defines a plurality of n structural circles C,
Based on the set of structural circles C, a surface data creation unit that creates surface data of an object made of a rotating body and outputs this as 3D information;
It is constituted by.

(5) According to a fifth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first to fourth aspects described above,
The imaging condition input means inputs the focal length of the camera used for imaging as information indicating “distance f between viewpoint and projection plane”.

(6) According to a sixth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first to fourth aspects described above,
The imaging condition input means inputs the angle of view of the camera used for imaging as information indicating “distance f between viewpoint and projection plane”.

(7) According to a seventh aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first to fourth aspects described above,
The projection condition determining means uses the “part corresponding to the lower end surface of the object” and the “part corresponding to the upper end surface of the object” included in the object image as arc-shaped features.

(8) According to an eighth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first to fourth aspects described above,
The contour line extracting means performs processing for extracting a contour line based on the trace of the trace operation performed by the operator on the two-dimensional image.

(9) According to a ninth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the first to fourth aspects described above,
The contour line extracting means performs a process of automatically extracting the contour line based on the difference between the pixel values of the individual pixels constituting the two-dimensional image.

(10) According to a tenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the ninth aspect described above,
A tertiary body of a rotating body characterized in that the automatically extracted contour line is subjected to correction based on the trace operation trace performed by the operator on the two-dimensional image, and the corrected contour line is extracted. Original information restoration device.

(11) According to an eleventh aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the second or fourth aspect described above,
The parameter setting unit uses the angle θ between the optical axis L and the XY plane and the position of the intersection ξ between the optical axis L and the XY plane as parameters that define the optical axis L.

(12) According to a twelfth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the eleventh aspect described above,
The parameter setting unit presents that the setting operation for increasing / decreasing the angle θ is an operation for performing “shape correction of the circular projection image”, and the setting operation for changing the position of the intersection ξ “the position of the circular projection image” It is presented that the operation is for performing “correction”.

(13) According to a thirteenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the second or fourth aspect described above,
The parameter setting unit always sets the first reference circle as a circle on the XY plane, sets the second reference circle as a circle on the plane “Z = D”, and sets each reference circle as a parameter. , The radius of the second reference circle, and the value of D are used.

(14) According to a fourteenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the thirteenth aspect described above,
The parameter setting unit presents that the setting operation for increasing or decreasing the radius of the first reference circle and the radius of the second reference circle is an operation for performing “size correction of the circular projection image”, and sets the value D to The setting operation to increase / decrease is presented as an operation for performing “relative position correction of two circular projection images”.

(15) According to a fifteenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the thirteenth or fourteenth aspect described above,
The “part corresponding to the lower end surface of the object” included in the object image is the first arc-shaped feature, and the “part corresponding to the upper end surface of the object” included in the object image is the second arc-shaped feature. It is what I did.

(16) According to a sixteenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the fifteenth aspect,
The contour line extracting means extracts a contour line CCside having one point on the first circle projection image and one point on the second circle projection image as both end points.

(17) According to a seventeenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the third or fourth aspect described above,
The structural circle definition part
The tangent vector TT of the contour line CCside at the reference point PP is defined as a line segment on the projection plane S connecting the two points PP / QQ by defining the tip point QQ, and the tangent vector of the structural circle C at the corresponding point P T is defined as a line segment on an XYZ three-dimensional coordinate system connecting two points P / Q by defining the tip point Q.
Using the condition that “the points obtained by perspective-projecting the corresponding point P and the tip point Q onto the projection plane S with the viewpoint E as the reference coincide with the reference point PP and the tip point QQ, respectively”, the corresponding point P The calculation for obtaining the coordinate value on the XYZ three-dimensional coordinate system is performed.

(18) According to an eighteenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the seventeenth aspect described above,
The structural circle definition part
Define the coordinate value (xp, yp, h) of the corresponding point P and the coordinate value (xq, yq, h) of the tip point Q on the XYZ three-dimensional coordinate system as unknowns,
Projecting the known coordinate values (αpp, βpp) of the reference point PP and the known coordinate values (αqq, βqq) of the tip point QQ on the XYZ three-dimensional coordinate system defined on the αβ two-dimensional coordinate system defined on the projection plane S By using the position information of the surface S, an operation for converting into coordinate values (xpp, ypp, zpp) and (xqq, yqq, zqq) on the XYZ three-dimensional coordinate system is performed,
The first conditional expression −xp / yp = (yq−yp) / (xq−xp) indicating that the tangent vector T is a tangent at the corresponding point P of the structural circle C
The reference point PP and the tip point QQ are obtained by perspectively projecting the corresponding point P and the tip point Q onto the projection plane S with the viewpoint E defined by the known coordinate values (xe, ye, ze) as a reference. Xp = ((h−ze) · (xpp−xe)) / (zpp−ze) + xe
yp = ((h-ze). (ypp-ye)) / (zpp-ze) + ye
xq = ((h-ze). (xqq-xe)) / (zqq-ze) + xe
yq = ((h-ze). (yqq-ye)) / (zqq-ze) + ye
And the value of the unknown h is calculated by solving the obtained equation, and the calculated value of h is substituted into the second conditional expression to obtain the coordinate values xp and yp, and “Z = h” A structural circle C having a radius R = (xp ² + yp ² ) ^1/2 is defined on the plane.

(19) According to a nineteenth aspect of the present invention, in the three-dimensional information restoration apparatus for a rotating body according to the fourth aspect described above,
The structural circle definition unit defines the first reference circle and the second reference circle defined by the parameters set in the parameter setting unit at the time when the coincidence confirmation is obtained as a part of the structural circle, and the total (N + 2) structural circles are defined.

  (20) According to the twentieth aspect of the present invention, a computer program can be prepared and distributed so that the three-dimensional information restoration apparatus for a rotating body according to the first to twentieth aspects described above can be configured by a computer. It is what I did.

  In the three-dimensional information restoration apparatus according to the present invention, the three-dimensional object to be applied is limited to a rotating body, and processing using the characteristics of the rotating body is performed, so only one two-dimensional image of the object is used. In addition, the three-dimensional information of the object can be restored with a relatively easy work load.

  Hereinafter, the present invention will be described based on the illustrated embodiments. As described above, the feature of the present invention is that three-dimensional information about the original object is restored based on only one two-dimensional image. Therefore, in the invention, the application target is limited to an object made of a rotating body. This is because, in the first place, the two-dimensional image does not include direct information indicating the depth, so that the three-dimensional information of the object having an arbitrary three-dimensional shape is restored based on only one two-dimensional image. This is because it is very difficult. If the original object is limited to a rotating body, there is a clue to estimate the 3D shape by using the characteristic inherent to this rotating body (that is, the characteristic that a circle appears everywhere in the 3D shape). Will be obtained.

  The process of restoring three-dimensional information according to the present invention is roughly divided into a first half stage for determining projection conditions and a second half stage for creating three-dimensional information. Therefore, hereinafter, the first half stage will be described in §1, and the second half stage will be described in §2. Also, §3 describes the overall procedure of the present invention, and §4 describes the basic configuration of the restoration device according to the present invention.

<<< §1. First half: Determination of projection conditions >>>
The purpose of the first half is to determine the projection conditions. In order to explain the basic principle, when a two-dimensional image is obtained by photographing a three-dimensional object from a predetermined direction, the geometric relationship between the two-dimensional image and the three-dimensional object is described. deep.

  FIG. 1 is a perspective view showing such a geometric relationship. The coordinate axis of the XYZ three-dimensional coordinate system is shown on the left side of the figure, but here, the three-dimensional object 10 made of a rotating body is placed on the XY plane, and the central axis of this rotating body. The following description will be made on the assumption that “Z” coincides with the Z axis. In the figure, a pottery pot is depicted as a three-dimensional object 10 for convenience of explanation. Since this ridge is a rotating body, the bottom surface and the top surface are both included in a plane perpendicular to the Z axis, and form a circle having a center point on the Z axis. In particular, the bottom surface is included in the XY plane and becomes a circle centered on the origin O of the coordinate system.

  On the other hand, on the projection surface S, a two-dimensional image (rectangular image having two points U1 and U2 as diagonal points) obtained by photographing the three-dimensional object 10 from a predetermined direction is formed. The object image 20 is included in the two-dimensional image. Here, the point E drawn on the right side indicates the viewpoint, and the object image 20 on the projection plane S is obtained by perspectively projecting the three-dimensional object 10 onto the projection plane S with the viewpoint E as a reference. This is a projected image. Here, a perpendicular line (shown by an alternate long and short dash line) drawn from the viewpoint E to the projection plane S is called an optical axis L, and a leg of this perpendicular line is called a point G. Further, as shown in the figure, an αβ two-dimensional coordinate system is defined on the projection surface S, and an arbitrary point on the projection surface S is represented by a coordinate value (α, β).

  FIG. 2 is a plan view of the projection plane S shown in FIG. The two-dimensional image obtained on the projection surface S is a rectangular image with the two points U1 and U2 as diagonal points, and an object image 20 in the shape of a bowl is arranged on the background. In the case of the embodiment described here, the upper and lower sides of the rectangle constituting the contour of the two-dimensional image are parallel to the XY plane. The point G is the center point of this rectangular two-dimensional image, but it is not necessarily the point located at the center of the eyelid (although usually, the subject is placed at the center of the screen when shooting with the camera). Therefore, it is likely that the center point G of the two-dimensional image is located near the center of the eyelid). An arbitrary point M on the two-dimensional image is represented by a coordinate value M (αm, βm).

  Actually, an image obtained when the three-dimensional object 10 is photographed from a predetermined direction with a camera is basically obtained by perspectively projecting the three-dimensional object 10 onto the projection plane S shown in FIG. This is a two-dimensional image. Here, the optical axis L coincides with the optical axis of the optical system of the camera used for photographing, and the point G becomes the center point of the two-dimensional image obtained by photographing. The distance f between the viewpoint E and the point G matches the focal length of the camera used for shooting. Therefore, a two-dimensional image obtained by photography is theoretically equivalent to a projection image obtained on the projection plane S under a predetermined projection condition as shown in FIG.

  An object of the present invention is to restore the three-dimensional information of the original three-dimensional object 10 based on an object image 20 (for example, a photographic image) as shown in FIG. Of course, the object image 20 shown in FIG. 2 is merely a two-dimensional image and does not include any direct information about the depth. However, paying attention to the condition that the three-dimensional object 10 that is the basis of the object image 20 is a rotating body, the object image 20 includes indirect information about the depth. The present invention intends to restore the three-dimensional information of the original three-dimensional object 10 using this indirect information as a clue.

  The purpose of the first half stage described in Section 1 is to determine the projection conditions shown in FIG. The projection conditions determined here are the position of the projection plane S (a broad position including the orientation) when the position of the three-dimensional object 10 is used as a reference, and the position of the viewpoint E. In the case of the projection system shown in FIG. 1, if the positions of the projection plane S and the viewpoint E on the XYZ three-dimensional coordinate system can be uniquely determined, the object obtained by projecting the three-dimensional object 10 arranged on the origin O The shape and size of the image 20 are uniquely determined. In other words, if the position of the projection plane S changes, the shape and size of the obtained object image 20 will change. Even if only the position of the projection surface S is determined, if the position of the viewpoint E changes, the shape and size of the obtained object image 20 will also change. Therefore, the projection conditions for obtaining a specific object image 20 based on the three-dimensional object 10 arranged on the origin O are the positions of the projection plane S and the viewpoint E.

  Therefore, in this first half stage, a process for determining projection conditions (positions of the projection plane S and the viewpoint E) at the time of photographing the object image 20 as shown in FIG. I do. In other words, this process can be said to be a process of estimating the position and orientation of the camera at the time of shooting.

  FIG. 3 is a front view of the projection system shown in FIG. Here, the floor surface XY is an XY plane in the XYZ three-dimensional coordinate system, and the right direction in the figure is the Y-axis direction. The three-dimensional object 10 made of a rotating body is arranged on the floor surface XY so that the center axis thereof is at the Z-axis position. In the case of this example, the projection surface S is a surface orthogonal to the paper surface of the drawing, and therefore is indicated by a single line on the drawing. A thick line portion drawn on the projection surface S indicates a position where the object image 20 is formed. The object image 20 is a projection image obtained by perspectively projecting the three-dimensional object 10 onto the projection plane S with the viewpoint E as a reference.

  The optical axis L indicated by the alternate long and short dash line coincides with a perpendicular drawn from the viewpoint E to the projection plane S and corresponds to the optical axis of the camera at the time of photographing. In other words, the projection plane S is always defined as a plane orthogonal to the optical axis L. As described above, the intersection point G between the optical axis L and the projection surface S is the center point of the rectangular two-dimensional image obtained by photographing. Here, for convenience of explanation, the optical axis L is further extended, the intersection with the XY plane is denoted by ξ, and the angle formed with the XY plane is denoted by the elevation angle θ. In the present application, the “position” with respect to the projection plane S and the optical axis L is used in a broad sense including its direction. For example, even if the position of the intersection ξ is the same, if the elevation angle θ changes, The position of the optical axis L also changes.

  As is clear from FIG. 3, the shape and size of the object image 20 formed on the projection surface S are the position of the projection surface S (in other words, the position of the optical axis L) and the position of the viewpoint E. Dependent. For example, in the case of the eyelid shown in the figure, if the elevation angle θ of the optical axis L is increased, a photographed image in which the eyelid is viewed from above can be obtained, and the vertical dimension of the object image 20 is reduced. Become. Even if the position of the viewpoint E is brought close to the projection plane S, the vertical dimension of the object image 20 is similarly reduced. However, when the three-dimensional object 10 is an object having an arbitrary shape, it is extremely difficult to estimate the positions of the projection plane S and the viewpoint E from only the information of the object image 20.

  Therefore, if the inventor assumes that the three-dimensional object 10 is a rotating body, the position of the projection plane S and the viewpoint E can be estimated from only the information of the object image 20. I got the idea that it wasn't there. As described above, the rotating body has an inherent characteristic that a circle appears everywhere in the three-dimensional shape. For example, FIG. 4 is a perspective view of the three-dimensional object 10 having the shape of a ridge with the Z axis as a rotation axis. A circle Cbottom appears on the contour of the lower end surface of the heel, and the contour of the upper end surface is shown. The circle Ctop appears. Such unique characteristics also appear on the object image 20 on the projection plane S. Of course, since the object image 20 is a projection image, the circle Cbottom and the circle Ctop appear as an elliptical projection image. The position and shape of the elliptical projection image are the projection plane S and the viewpoint E. Gives valuable information to estimate the location.

  Here, what kind of geometric figure can be obtained when the circle C on the three-dimensional object 10 is projected onto the projection plane S will be considered. FIG. 5 is a perspective view showing a projection image C ′ obtained by parallel projecting the circle C on the XYZ three-dimensional coordinate system onto the projection plane S (referred to as a circle projection image because it is obtained by projecting a circle). FIG. 6 is a perspective view showing a projection image CC (also referred to as a circular projection image) obtained by perspectively projecting the circle C on the XYZ three-dimensional coordinate system onto the projection plane S. In either case, the two-dimensional circular projection image is obtained on the projection plane S in the same way, but since the projection methods are different between the two, the shapes of the obtained circular projection images are different from each other.

  First, in the parallel projection shown in FIG. 5, a vector V indicating the projection direction is determined, and projection is performed in a direction parallel to the vector V. The projection lines indicated by broken lines in the figure are all straight lines parallel to the vector V. For example, when a shadow of an object is formed on the ground by parallel rays such as sunlight, the shadow formed on the ground is a parallel projection image of the object. Since the parallel projection image of the circle C is a geometric ellipse, the circle projection image C ′ is also a geometric ellipse in the illustrated example.

  On the other hand, in the perspective projection shown in FIG. 6, a reference viewpoint E is determined, and projection is performed from the viewpoint E in the direction of seeing through the object. The projection lines indicated by broken lines in the figure are all straight lines passing through the viewpoint E. An image formed on the retina by the human naked eye observation or a photographed image by the camera is a perspective projection image of the object. The perspective projection image of the circle C is not necessarily a geometric ellipse, and in many cases is a distorted ellipse. Also in the illustrated example, the circular projection image CC is not a geometric ellipse, but a distorted ellipse.

  The two-dimensional image handled by the present invention is an image taken by a camera, and is an image obtained by perspectively projecting an object as shown in FIG. Therefore, the circular projection image of the circle Cbottom and the circle Ctop shown in FIG. 4 is not a geometric ellipse but a distorted ellipse. In other words, some information regarding the projection condition is included in the distortion of the circular projection image. In the present invention, processing for estimating the positions of the projection plane S and the viewpoint E is performed using information such as the shape, size, position, and degree of distortion of the circular projection image. The principle will be described with reference to FIG.

  FIG. 7 is a front view of the projection system for illustrating the basic principle of the method for determining the positions of the projection plane S and the viewpoint E according to the present invention. The main components in this figure are the same as the components shown in FIG. That is, the floor surface XY is an XY plane in the XYZ three-dimensional coordinate system, and the right direction in the figure is the Y-axis direction. A projection plane S indicated by one straight line is a plane orthogonal to the drawing sheet. The optical axis L indicated by the alternate long and short dash line coincides with the vertical line drawn from the viewpoint E to the projection plane S (the point G is a vertical leg) and corresponds to the optical axis of the camera at the time of photographing. The projection surface S is a plane orthogonal to the optical axis L. A point ξ is an intersection between the optical axis L and the XY plane, and an elevation angle θ is an angle formed by the optical axis L and the XY plane.

  In FIG. 7, the three-dimensional object 10 is not shown. This is because no specific shape information about the three-dimensional object 10 has been obtained at the initial stage of implementing the present invention. However, since the application target of the present invention is limited to an object made of a rotating body, in the example shown here, the three-dimensional object 10 is a rotating body having the Z axis as the central axis in the XYZ three-dimensional coordinate system. The minimum information of being arranged on the floor surface XY is obtained. In FIG. 7, the projection plane S and the viewpoint E are drawn at predetermined positions. At this stage, the positions of the projection plane S and the viewpoint E are not yet determined, and the projection plane S and the viewpoint E shown in the figure are not yet determined. Is provisional.

  Now, let us define two reference circles on the virtual space as shown in FIG. The first reference circle Cbottom corresponds to the contour circle Cbottom of the lower end surface of the three-dimensional object 10 shown in FIG. 4, and the second reference circle Ctop is the upper end surface of the three-dimensional object 10 also shown in FIG. Corresponds to the contour circle Ctop. Of course, since no specific three-dimensional information of the actual three-dimensional object 10 is obtained at this stage, the value of the radius Rbottom of the first reference circle Cbottom and the value of the radius Rtop of the second reference circle Ctop. The distance D between both reference circles may be flawless at this point. However, based on the minimum information that the three-dimensional object 10 is a rotating body having the Z axis as the central axis in the XYZ three-dimensional coordinate system and is arranged on the floor XY, both reference circles Cbottom, Ctop is included in a plane perpendicular to the Z axis, and is a circle having a center point on the Z axis. Here, since the first reference circle Cbottom corresponds to the contour circle of the lower end surface of the three-dimensional object 10, the first reference circle Cbottom is made to be a circle on the floor surface XY, and the second reference circle Ctop is A circle on a plane defined by the expression “Z = D” (hereinafter referred to as “Z = D” plane) is used.

  Here, as shown in FIG. 7, when the first reference circle Cbottom and the second reference circle Ctop are perspective-projected onto the projection surface S with the viewpoint E as a reference, the first reference circle Cbottom and the second reference circle Ctop are projected on the projection surface S. , And a second circular projection image CCtop are obtained. In the figure, these circular projection images are drawn as thick lines on a straight line indicating the projection plane S. As described above, these circular projection images become distorted ellipses.

  Here, the given two-dimensional image (a photographed image of the three-dimensional object 10) is pasted on the projection plane S. At this time, the alignment is performed so that the center point of the two-dimensional image coincides with the foot G of the perpendicular line drawn from the viewpoint E to the projection plane S. Then, when the first circle projection image CCbottom and the second circle projection image CCtop are arranged on the pasted two-dimensional image so as to overlap, for example, a result as shown in FIG. 8 is obtained. The point G is the center point of this two-dimensional image, and the optical axis L is a straight line passing through the point G and orthogonal to the projection plane S.

  On the two-dimensional image, an object image 20 corresponding to the three-dimensional object 10 is included, but at present, there is no correlation between the object image 20 and each of the circular projection images CCbottom and CCtop. Is not seen. As described above, the first reference circle Cbottom corresponds to the contour circle Cbottom of the lower end surface of the three-dimensional object 10 shown in FIG. 4, and the second reference circle Ctop is the same as the three-dimensional object shown in FIG. 10, the first circular projection image CCbottom is originally “the portion 21 corresponding to the lower end surface of the object (first The second circular projection image CCtop corresponds to “a portion 22 corresponding to the upper end surface of the object (referred to as a second arcuate feature)” included in the object image 20. Must match.

  However, as shown in FIG. 8, the result in which no coincidence was found was obtained in the projection system shown in FIG. 7 in the positions of the projection plane S and the viewpoint E, the radius Rbottom of the first reference circle Cbottom. This is because the value, the value of the radius Rtop of the second reference circle Ctop, and the value of the distance D between both reference circles are frank. Of course, in the initial stage of carrying out the present invention, information on these positions and values is hardly obtained (although rough information may be obtained by observing the projection image 20), In the initial stage, these positions and values must be set to be frank. However, if the result of the superimposed display as shown in FIG. 8 is examined, it is possible to perform correction in a direction in which a final match can be obtained with respect to these pieces of information that were initially set to be frank. Become.

  For example, in the case of the specific example shown in FIG. 8, when attention is paid to the shapes of the bi-circular projection images CCbottom and CCtop, it can be seen that each has a shape that is narrower in the vertical direction than the respective arc-shaped features 21 and 22. . This means that the elevation angle θ under the currently set projection conditions is too small than the elevation angle under actual imaging conditions. That is, it can be recognized that the object image 20 shown in FIG. 8 is actually an image taken at a steep elevation angle that looks down from above the direction of the optical axis L shown in FIG. Therefore, in this case, it is only necessary to correct the direction in which the elevation angle θ is increased.

  In the case of the specific example shown in FIG. 8, the size (horizontal width) of the first circular projection image CCbottom substantially matches the size of the first arcuate feature 21, but the size of the second circular projection image CCtop. Is too large compared to the size of the second arcuate feature 22. This means that the setting value of the radius Rbottom is almost appropriate, but the setting value of the radius Rtop is too large. Therefore, in this case, it is only necessary to make a correction in a direction to decrease the set value of the radius Rtop.

  On the other hand, paying attention to the position-related displacement, in the case of the specific example shown in FIG. This means that the position of the optical axis L (the position of the point G shown in FIG. 8) under the currently set projection conditions is shifted to the left from the actual photographing position. Therefore, in this case, a correction may be made to shift the position of the intersection point ξ shown in FIG.

  Further, in the specific example shown in FIG. 8, it can be seen that the first circular projection image CCbottom and the second circular projection image CCtop are too close. This means that the set value of D shown in FIG. 7 is too small. Therefore, in this case, it is only necessary to correct the direction in which the set value of D is increased.

  Here, it will be examined how the parameters involved in the determination of the projection plane S and the viewpoint E affect the circular projection image obtained on the projection plane S. First, as described in the above example, the elevation angle θ of the optical axis L can be said to be a parameter that governs the thickness (roundness) of a circular projection image that is substantially elliptical. That is, as the elevation angle θ is set to be larger, the reference circle is looked down from directly above, so that the circle projection image becomes closer to a circle. Conversely, the smaller the elevation angle θ is set, the more the circular projection image is crushed. Thus, the elevation angle θ of the optical axis L can be said to be a parameter intuitively linked to the shape of the circular projection image.

  On the other hand, the position of the intersection ξ between the optical axis L and the XY plane can be said to be a parameter governing the position of the circular projection image as described in the above example. That is, when it is desired to move the circular projection image vertically and horizontally on the projection plane S, the position of the intersection ξ may be moved on the XY plane.

  Next, consider the rotation angle φ of the optical axis L. 9 is a top view of the projection system shown in FIG. 7, and the Z axis is an axis perpendicular to the paper surface at the origin O. FIG. The two sets of reference circles Cbottom and Ctop are both drawn as perfect circles in FIG. In the figure, the two pairs of reference circles Cbottom and Ctop are projected on the projection surface Sy based on the optical axis Ly along the Y axis, and the projection surface based on the optical axis Lw along the W axis. A case of perspective projection on Sw is depicted. Here, the points Gy and Gw are intersections between the optical axes and the projection planes, and the W axis is an axis obtained by rotating the Y axis on the XY plane by the rotation angle φ with respect to the origin O. As can be easily imagined from the figure, the circular projection image obtained on the projection surface Sy and the circular projection image obtained on the projection surface Sw are exactly the same. The same applies to a case where a three-dimensional object made of a rotating body is arranged so that the central axis is on the Z axis instead of the reference circles Cbottom and Ctop. That is, as long as the rotating body is projected, the parameter of the rotation angle φ of the optical axis L is a parameter that does not affect the projected image and is a parameter that does not need to be considered in the present invention.

  Next, consider the parameter of the position of the projection surface S on the optical axis L. FIG. 10 is a front view of the projection system for explaining the influence of the position of the projection plane S on the optical axis L on the projection image. The projection plane S in the projection system shown in FIG. 3 is moved to the position of the projection plane S ′. The moved state is shown. Since the projection plane is always a plane orthogonal to the optical axis, the projection plane S ′ is a plane parallel to the projection plane S, and the intersection point with respect to the optical axis L has moved from the point G to the point G ′. In this case, when the projection images of the three-dimensional object 10 obtained on the projection planes S and S ′ are compared, it can be seen that they are similar. In other words, this parameter is a parameter that determines the magnification of the entire projection image obtained on the projection plane.

  After all, in implementing the present invention, it is not necessary to consider the parameter of the position of the projection surface S on the optical axis L. This is because, in practice, a two-dimensional image given as an application target of the present invention is an image enlarged or reduced at an arbitrary magnification, and is not the same as the size of a perspective projection image at the time of photographing. Since it is usually unknown how much magnification a given two-dimensional image has with respect to a perspective projection image at the time of shooting, a parameter called the position of the projection surface S on the optical axis L It is meaningless to determine exactly. Therefore, this parameter may be set arbitrarily. For example, it is sufficient to determine in advance that the projection plane S is defined such that the point G is located at a position away from the intersection point ξ by a predetermined default distance. In actual calculation processing, the factor of the magnification of the entire projected image is a factor incorporated in the values of the radius Rbottom and Rtop of each reference circle and the distance D of both reference circles.

  Finally, consider a parameter called the distance f between the projection surface S and the viewpoint E. As described above, this distance f corresponds to the focal length of the camera used at the time of photographing. The focal length f increases when photographing using a telephoto lens, and the focal point occurs when photographing using a wide-angle lens. The distance f becomes smaller. The focal length f of the camera is a factor that is synonymous with the angle of view of the camera (the angle within the shooting range). The larger the focal length f, the narrower the angle of view, and the smaller the focal length f, Become wider. For example, in FIG. 7, when the distance f increases, the viewpoint E comes to a position away from the projection plane S, and the angle formed by two projection lines indicated by broken lines becomes smaller. On the contrary, when the distance f becomes smaller, the viewpoint E comes to a position closer to the projection plane S, and the angle formed by the two projection lines indicated by the broken line becomes larger.

  Actually, this parameter f is a complex parameter that governs the position, size, and shape of the projected image obtained on the projection plane S. Therefore, in FIG. 7, when the value of the distance f is changed, the positions, sizes, and shapes of the respective circular projection images CCbottom and CCtop obtained on the projection plane S are changed. Thus, the parameter of the distance f between the projection surface S and the viewpoint E is a parameter that is very difficult to handle. Therefore, in the present invention, the distance f is not handled as a variable parameter, but is handled as a known amount given as one of the imaging conditions. As described above, when the three-dimensional object 10 is shot with a general camera, the distance f between the projection surface S and the viewpoint E is a value corresponding to the focal length of the camera. Therefore, if data on the focal length of the camera used at the time of shooting remains, the distance f can be given as a known amount.

  Further, as described above, the focal length f of the camera is a factor that is synonymous with the angle of view of the camera, and the distance f can be calculated if information on the angle of view of the camera used during shooting remains. is there. That is, the angle of view of the camera is normally given as a parallax angle when the diagonal points U1 and U2 of the two-dimensional image obtained on the projection plane S as shown in FIG. The distance f can be calculated based on the actual size between U1 and U2.

  As described above, several parameters related to the determination of the projection plane S and the viewpoint E are examined. Eventually, in the projection system shown in FIG. 7, the parameters to be considered for determining the geometric condition are “light It can be seen that “the position of the axis L”. Here, as described above, the “position” with respect to the optical axis L has a broad meaning including its orientation, and is specifically determined by the position of the intersection ξ on the XY plane and the elevation angle θ. The The rotation angle φ of the optical axis L need not be considered as described in the top view of FIG. Further, as described with reference to FIG. 10, the parameter of the position of the projection surface S on the optical axis L is simply a parameter that influences the magnification of the entire projection image, and does not need to be considered (set to an arbitrary value). It does n’t matter) On the other hand, the distance f can be handled as a known amount given as one of the photographing conditions. Thus, if the “position of the optical axis L” (elevation angle θ and intersection ξ) can be determined, the projection plane S and viewpoint E in the projection system shown in FIG. 7 can be determined.

  That is, first, an optical axis L that passes through the intersection ξ and forms an elevation angle θ is determined (the rotation angle φ does not need to be taken into account, so the optical axis L may be defined as a straight line included in the YZ plane, for example). A point G is determined at an arbitrary position on the optical axis L (for example, a predetermined distance d may be determined in advance, and the point G may be defined at a position separated from the intersection ξ by d). The projection plane S can be uniquely determined as a plane orthogonal to the. Furthermore, using the distance f given as a known amount, the viewpoint E can be uniquely determined as a point on the optical axis L that is separated from the point G by the distance f.

  On the other hand, since the first reference circle Cbottom shown in FIG. 7 is a circle on the XY plane centered on the origin O, it is uniquely determined only by defining its radius Rbottom. Further, since the second reference circle Ctop is a circle on the “Z = D” plane centered on a point on the Z axis, it is uniquely determined only by defining the radius Rtop and the distance D. Thus, the factors that determine the two reference circles are the three values Rbottom, Rtop, and D.

  From the above, in the projection system shown in FIG. 7, the parameters to be set when obtaining the circular projection images of the two reference circles Cbottom and Ctop on the projection plane S are the position of the intersection ξ, the elevation angle θ, and the radius Rbottom. , Radius Rtop and distance D. By changing the settings of these five parameters, the shapes, sizes, and positions of the circular projection images CCbottom and CCtop obtained on the projection plane S as illustrated in FIG. 8 can be changed.

  FIG. 11 is a diagram showing the effects of these five parameters on the circular projection images CCbottom and CCtop. First, as described above, the first parameter “elevation angle θ of the optical axis L” is a factor that governs the shapes (roundness) of both circular projection images CCbottom and CCtop. Further, the “position of the intersection ξ” that is the second parameter is a factor that governs the position of both the circular projection images CCbottom and CCtop on the projection plane S. Further, the “radius Rbottom, Rtop” as the third and fourth parameters is a factor governing the size of the circular projection images CCbottom, CCtop, and the “distance D” as the fifth parameter is the circular projection image CCbottom. , CCtop is a factor governing the mutual positional relationship (the distance between the two in the vertical direction).

  Considering that these five parameters are factors having the characteristics as described above, for example, at the initial stage (the stage where the above parameters are set to the parameters), for example, a superimposed display as shown in FIG. Even if it is obtained, each parameter is set so that the first circular projection image CCbottom matches the first arcuate feature 21 and the second circle projection image CCtop matches the second arcuate feature 22. It is possible to correct the set value.

  FIG. 12 is a plan view showing a state in which such a match is obtained. In this way, the fact that a match is obtained means that the projection system determined by the set values of the five parameters at that time coincides with the projection system at the time of shooting for obtaining the object image 20. To do. For example, if the projection system as shown in FIG. 7 is determined by the set values of the five parameters at the time when the superimposed display matches, the projection system shown in FIG. This is consistent with the projection system.

  However, in the present invention, since the parameter of the position of the projection surface S on the optical axis L (the parameter that affects the magnification of the entire projection image) is set to an arbitrary value, strictly speaking, the position of the projection surface S Is different from the position at the time of shooting. Therefore, if the three-dimensional information of the original object 10 is restored based on the object image 20 on the projection surface S on the assumption of the projection system of FIG. 7, the size of the restored three-dimensional image is the original cubic It does not match the size of the original object 10. However, this is merely a problem of image magnification, and since the magnification of the given two-dimensional image itself is not usually the correct magnification of the projected image at the time of shooting (for example, a two-dimensional image as a photograph) ), The size of the object image 20 changes depending on the enlargement magnification of the photograph), and no practical problem occurs.

  As can be seen from the example shown in FIG. 8, the circular projection images CCbottom and CCtop superimposed and displayed on the projection surface S are elliptical closed curves, but the arc-shaped features 21 and 22 on the object image 20 are , It does not necessarily become a closed curve. For example, in the case of the example shown in FIG. 8, the arc-shaped feature 22 corresponding to the upper end surface of the object is a so-called phlegm mouth portion, so that it can be recognized as a closed curve, and the entire circular projection image CCtop can be recognized. Can be confirmed. However, since the back side portion of the arc-shaped feature portion 21 corresponding to the lower end surface of the object is hidden, confirmation of matching with the circular projection image CCbottom is performed only for a portion on the near side.

  Further, in practice, it is sufficient that the matching between the two is performed with a predetermined accuracy. In the case of rotating earthenware such as pots, it is common to make them using lokuro, so the top and bottom surfaces are very close to a perfect circle. However, as long as the three-dimensional object 10 is a craft, the upper end surface and the lower end surface are not completely perfect circles. In addition, when the resolution of a given two-dimensional image is low, the accuracy with which the arc-shaped feature on the object image 20 can be viewed is limited. Therefore, in practical use, when these points are considered and the operator determines that the two overlap each other with an accuracy within an allowable range, the determination of coincidence may be made.

<<< §2. Second half: Creation of 3D information >>>
Next, the basic principle of the latter half of the present invention will be described. The purpose of the first half stage described above is to determine the projection conditions as shown in FIG. 7, that is, the projection plane S and the viewpoint E, and when the coincidence determination on the screen as shown in FIG. 12 is obtained. This objective has been achieved. At this time, the given two-dimensional image is arranged on the projection surface S, and the center point of the two-dimensional image coincides with the point G (the position of the optical axis). Further, the reference circles Cbottom and Ctop shown in FIG. 7 respectively coincide with the contours of the lower end surface and the upper end surface of the three-dimensional object 10 to be restored. In other words, only the information about the upper and lower end surfaces of the three-dimensional object 10 to be restored is obtained at the stage where the first half stage described in §1 is completed. The purpose of the second half stage described in §2 is to create three-dimensional information existing between the upper and lower end faces.

  The process performed at the beginning of the latter half is a process of extracting the contour line on one side surface of the object image 20 arranged on the projection surface S. Specifically, in the diagram shown in FIG. 12, processing is performed to extract the right side outline or the left side outline connecting the upper surface and the lower surface of the eyelid shown as the object image 20. FIG. 13 is a diagram illustrating a state in which a contour line CCside (indicated by a thick line) on the right side surface of the bag is extracted. This contour line CCside is a line connecting the circular projection images CCtop and CCbottom. Since the object image 20 is basically a projection image of a rotating body, in principle, the right-side contour line and the left-side contour line have a mirror image relationship, so if only one of them is extracted. It is enough. Of course, in order to improve accuracy, it is possible to obtain an average contour line considering both mirror images after extracting both contour lines.

  The most direct method for extracting the contour line CCside is a method for extracting a contour line based on the trace of the trace operation performed by the operator on the two-dimensional image. For example, as shown in FIG. 12, the state in which the object image 20 is arranged on the projection surface S is displayed on the display screen (the superimposed display of the circular projection images CCtop and CCbottom is not always necessary), and some input device is used. Then, the operator may perform an operation of tracing the contour line on one side surface of the object image 20 and sequentially record the coordinate values of the locus. At this time, if a method such as displaying a portion where the trace is completed with a thick line is taken, the progress of the trace operation can be presented to the operator in real time, and when the trace operation is completed, the display screen as shown in FIG. An image will be displayed. In the illustrated example, an αβ two-dimensional coordinate system is defined on the projection plane S, and the extracted contour line CCside is data consisting of a set of points having coordinate values in the form of (α, β). Defined.

  On the other hand, it is also possible to automatically execute the contour CCside extraction operation by a computer. A two-dimensional image as shown in FIG. 12 is configured by a pixel array on an αβ two-dimensional coordinate system, and the object image 20 is expressed by pixel values of individual pixels. Therefore, it is possible to cause the computer to execute a process of automatically extracting the contour line CCside based on the difference between the pixel values of the individual pixels constituting the two-dimensional image (difference between the background portion and the heel portion). Since such a technique for automatically extracting the contour line is a known technique, a detailed description thereof is omitted here.

  Now, when the contour line CCside of the one side surface of the object image 20 arranged on the projection surface S can be extracted in this way, the information of the two-dimensional contour line CCside is used to restore the three-dimensional information. That is, as shown in FIG. 7, since the projection plane S and the viewpoint E have already been determined by the process in the first half, by performing perspective projection onto the projection plane S with the viewpoint E as a reference, two projections on the projection plane S are obtained. The three-dimensional information of the rotator so that the three-dimensional contour line CCside can be obtained is created at a position about the Z axis on the XYZ three-dimensional coordinate system.

  For example, assume that a three-dimensional contour Cside can be obtained on an XYZ three-dimensional coordinate system as shown in FIG. The three-dimensional contour line Cside shown in FIG. 14 corresponds to the two-dimensional contour line CCside shown in FIG. 13, and the three-dimensional contour line Cside is perspectively projected onto the projection plane S with the viewpoint E as a reference. The geometric relationship is that a two-dimensional contour line CCside is obtained on the projection plane S. The three-dimensional contour line Cside shown in FIG. 14 is a line that can be grasped as a contour line when observing the eyelid from the viewpoint E, and for the eyelid having a three-dimensional shape, 1 drawn on the side surface thereof. It's just a book line. If such a three-dimensional contour Cside can be defined, by defining the circles C1 to Cn in contact with the contour Cside as shown in the figure, a wire frame indicating the three-dimensional shape of the heel is formed. Three-dimensional information can be created based on this wire frame.

  Since the individual circles C1 to Cn constituting the wire frame are circles that define the three-dimensional structure of the object to be restored, they are referred to as “structural circles” here. FIG. 14 shows a state where n structural circles C1, C2, C3,..., Ci,..., Cn are defined between the reference circle Cbottom and the reference circle Ctop. These structural circles C1 to Cn are all included in a predetermined plane orthogonal to the Z axis and have a center point on the Z axis. In practice, it is preferable that the reference circles Cbottom and Ctop are also handled as part of the structure circle, and the three-dimensional information of the object to be restored is defined by a total of (n + 2) structure circles. Here, the values of the radii Rbottom and Rtop of the reference circles Cbottom and Ctop are already determined in the first half process described in §1, but the n structural circles C1, C2, C3,. The radius R1, R2, R3,..., Ri,..., Rn for Cn is determined by the condition that each structural circle is in contact with the contour line Cside.

  Incidentally, the three-dimensional contour Cside shown in FIG. 14 cannot be obtained directly from the two-dimensional contour CCside shown in FIG. This is because, in order to define the contour Cside on the XYZ three-dimensional coordinate system, three-dimensional information is required, whereas the contour CCside obtained on the projection plane S contains only two-dimensional information. Because it is not. In other words, when a known three-dimensional figure exists on the XYZ three-dimensional coordinate system, the projection plane S can be obtained by performing perspective projection on the three-dimensional figure as long as the projection plane S and the viewpoint E are determined. It is possible to obtain a two-dimensional projection image of the three-dimensional figure on the top. However, conversely, when a known two-dimensional figure exists on the projection surface S, even if the viewpoint E is determined, the three-dimensional figure can be obtained by perspective projection based on the viewpoint E. Cannot be uniquely determined on the XYZ three-dimensional coordinate system.

  However, in the case of the present invention, since there is a major premise that the original object to be restored is a rotating body, by incorporating this major premise into the condition, the two-dimensional contour CCside shown in FIG. The three-dimensional contour line Cside shown in FIG. The principle and specific procedure will be described below.

  Now, as shown in the perspective view of FIG. 15, it is assumed that a three-dimensional object 10 (１０) made of a rotating body is arranged on an XYZ three-dimensional coordinate system. Here, it is assumed that the central axis of the ridge coincides with the Z axis and the lower end surface coincides with the XY plane. In other words, the illustrated basket is placed on the floor XY with the origin O as the center. Then, if the viewpoint E and the optical axis L are defined as shown in the figure, and this eyelid is perspective-projected on a predetermined projection surface S, an object image 20 as shown in FIG. 16 is obtained on the projection surface S, for example. Will be. Here, the projection surface S is an arbitrary plane orthogonal to the optical axis L.

  In the contour line extraction process described above, a two-dimensional contour line CCside is extracted from the right side surface of the object image 20 shown in FIG. A three-dimensional contour Cside indicated by a broken line in FIG. 15 is a contour corresponding to the two-dimensional contour CCside, and is a line indicating a position observed as the rightmost side of the eyelid when viewed from the viewpoint E. It can be said. As described above, as long as the projection plane S and the viewpoint E are determined, the two-dimensional contour CCside can be obtained from the three-dimensional contour Cside, but the reverse is not possible.

  Therefore, as shown in FIG. 15, a structural circle C is defined at an arbitrary height h of the ridge 10. This structural circle C is included in the “Z = h” plane and has a center point on the Z axis, and its radius R is equal to the radius at the height h of the ridge 10. A point P is defined at the intersection position between the structural circle C and the three-dimensional outline Cside. If the X coordinate value of this point P is xp and the Y coordinate value is yp, the point P is a point indicated by a three-dimensional coordinate value (xp, yp, h). On the other hand, if the projection point on the projection plane S corresponding to the point P is a point PP, the point PP is one point on the two-dimensional contour line CCside as shown in FIG. Here, if an αβ two-dimensional coordinate system is defined on the projection plane S as shown in the figure, and the α coordinate value of the point PP is αpp and the β coordinate value is βpp, the point PP is (αpp, βpp) This is a point indicated by the two-dimensional coordinate value.

  Again, the point PP (αpp, βpp) can be obtained from the point P (xp, yp, h), but conversely, the point P (xpp, yp, h) is obtained from the point PP (αpp, βpp). It cannot be determined uniquely. The relationship that the point P is located on the straight line connecting the viewpoint E and the point PP is established between the point PP and the point P, but the depth information is lost in the object image 20 on the projection plane S. Therefore, it is impossible to specify where the point P exists on this straight line. In other words, if there is any information that can cover the lost depth information, the position of the point P can be specified.

  Therefore, as described above, consider the main premise that the cage 10 shown in FIG. 15 is a rotating body. The inventor of the present application has found that the information on the lost depth can be covered by adding the condition that “the original three-dimensional object is a rotating body”.

  For this purpose, first, as shown in FIG. 15, a structural circle C that is a tangent vector T at a point P is defined. In order to define such a tangent vector T, a tip point Q may be determined as shown in the figure. Since the tangent vector T is a tangent to the structural circle C, it is naturally a vector included in the “Z = h” plane, and the line segment P / Q is included in the “Z = h” plane. Therefore, the tip point Q is a point indicated by a three-dimensional coordinate value (xq, yq, h). On the other hand, if a projection vector on the projection plane S corresponding to the tangent vector T is obtained with the viewpoint E as a reference, a projection vector TT is obtained as shown in FIG. In order to define such a projection vector TT, the tip point QQ may be determined. The tip point QQ is a projection point obtained by projecting the tip point Q on the projection plane S, and is a point indicated by a two-dimensional coordinate value (αqq, βqq).

  After all, the tangent vector T shown in FIG. 15 is a three-dimensional vector defined on the XYZ three-dimensional coordinate system, whereas the projection vector TT shown in FIG. 16 is defined on the αβ two-dimensional coordinate system. This means a two-dimensional vector, and the line segment PP / QQ is included in the projection plane S. The point to be noted here is that the projection vector TT shown in FIG. 16 is a tangent to the contour line CCside at the point PP.

  The reason can be easily understood by considering the contact surface of the flange 10 at the point P in the perspective view of FIG. That is, if one plane is brought into contact with the ridge 10 at the position of the point P, the tangent vector T is naturally included on this tangent plane. Now, consider how this tangent surface looks on the projection shown in FIG. The contour line Cside indicated by a broken line in FIG. 15 corresponds to the contour line CCside in the projection view of FIG. 16, so that the contact surface that contacts the ridge 10 at the point P shown in FIG. Above, it corresponds to the tangent line that touches the contour line CCside at the point PP. Since the tangent vector T is a vector included in the tangent plane, the projection vector TT that is a projection image thereof is a vector included in a straight line corresponding to the tangent plane, and eventually the contour line CCside at the point PP is It will be tangent. Therefore, the projection vector TT can also be called a tangent vector TT.

  FIG. 17 is a perspective view showing the positional relationship between the three-dimensional tangent vector T shown in FIG. 15 and the two-dimensional tangent vector TT shown in FIG. Here, the tangent vector T is a three-dimensional tangent vector that contacts the structural circle C at the point P, and the tangent vector TT is a two-dimensional tangent vector that contacts the contour CCside at the point PP.

  As described above, in FIG. 17, if only the projection condition that “the point PP is obtained by projecting the point P onto the projection surface S with the viewpoint E as a reference” is used, the point PP (2 having only two-dimensional coordinates is used. Based on αpp, βpp), the corresponding point P (xp, yp, h) having three-dimensional coordinates cannot be obtained. However, by adding as a condition “relationship between projection vector T and TT” that is established under the premise that “壺 10 is a rotating body”, corresponding point P (xp, yp) corresponding to point PP (αpp, βpp) , H).

  That is, the corresponding point P corresponding to the point PP is “a structural circle C included in a predetermined plane orthogonal to the Z axis on the XYZ three-dimensional coordinate system, having a center point on the Z axis, and passing through the corresponding point P. A two-dimensional vector TT obtained on the projection plane S is obtained by obtaining a tangent vector T at the corresponding point P with respect to the structural circle C, and perspectively projecting the tangent vector T onto the projection plane S with the viewpoint E as a reference. , A tangent to the contour line CCside at the point PP ”can be added. Here, the tangent vector TT of the contour line CCside at the point PP is defined as a line segment on the projection plane S connecting the two points PP / QQ by defining the tip point QQ, and the structure circle C of the corresponding point P is defined. If the tangent vector T is defined as a line segment on the XYZ three-dimensional coordinate system connecting the two points P / Q by defining the tip point Q, the additional condition is that “the corresponding point P and the tip point Q are In other words, the points obtained by perspective projection onto the projection surface S with the viewpoint E as a reference coincide with the points PP and QQ, respectively.

  Subsequently, according to the principle described above, the corresponding point P (xp, yp, h) having three-dimensional coordinates can be obtained by calculation based on the point PP (αpp, βpp) having only two-dimensional coordinates. 18 to 20 will be used for explanation.

First, the equation of the structural circle C in the XYZ three-dimensional coordinate system is expressed by equations (1) and (2) as shown in FIG. Here, R is the radius of the structural circle C, and h is a value indicating the arrangement position (height) of the structural circle C as shown in FIG. Next, after solving equation (1) for Y, both sides are differentiated by X to obtain equation (3) shown in FIG. 18 (b). Here, the differential value dY / dX is a value indicating the direction in the “Z = h” plane of the tangent of the structural circle C at the point of the coordinate value (X, Y, h) on the structural circle C. . Therefore, the orientation of the tangent vector T in the “Z = h” plane is obtained by substituting the XY coordinate value of the corresponding point P (xp, yp, h) into the equation (3), and the corresponding point P By applying the expression “xp ² + yp ² = R ² ” indicating the condition which is the above one point, the expression (4) as shown in FIG. On the other hand, considering that the tangent vector T is represented by a line segment having two points P (xp, yp, h) and Q (xq, yq, h) as both end points, “Z = The orientation in the “h” plane can also be expressed as in equation (5). Therefore, by setting the right side of equation (4) and the right side of equation (5) equal, as shown in the bottom row of FIG. 18 (c),
-Xp / yp = (yq-yp) / (xq-xp) The following formula (6) is obtained.
This expression (6) is a conditional expression indicating that the tangent vector T is a tangent at the point P on the structure circle C.

  Next, consider the equations of the projection lines Lp and Lq indicated by broken lines in FIG. Before that, since the coordinate values of the point PP (αpp, βpp) and the point QQ (αqq, βqq) on the projection plane S are coordinate values on the αβ two-dimensional coordinate system, these are the coordinates on the XYZ three-dimensional coordinate system. Try to convert it to a value. The position of the projection plane S on the XYZ three-dimensional coordinate system has already been determined in the first half stage described in §1, and the projection plane S can be expressed by an equation using XYZ. Therefore, the process of converting the coordinate value on the αβ two-dimensional coordinate system defined on the projection plane S into the coordinate value on the XYZ three-dimensional coordinate system can be performed as a simple coordinate conversion operation. PP (αpp, βpp) and QQ (αqq, βqq) can be converted into two-point PP (xpp, ypp, zpp) and QQ (xqq, yqq, zqq).

  The projected line Lp shown in FIG. 17 is a straight line passing through three points E (xe, ye, ze), PP (xpp, ypp, zpp), and P (xp, yp, h). When the equation of a straight line passing through two points in a three-dimensional space is applied as a straight line passing through E (xe, ye, ze) and PP (xpp, ypp, zpp), three equations shown in FIG. It can be expressed as (7-1), (7-2), (7-3). Here, t is a parameter. On the other hand, the projection line Lq shown in FIG. 17 is a straight line passing through three points E (xe, ye, ze), QQ (xqq, yqq, zqq), and Q (xq, yq, h). If the equation of a straight line passing through two points in a three-dimensional space is applied as a straight line passing through E (xe, ye, ze) and QQ (xqq, yqq, zqq), three equations shown in FIG. It can be expressed by (8-1), (8-2), (8-3). Here, s is a parameter.

Since the point P (xp, yp, h) is an intersection of the “Z = h” plane and the projection line Lp, substituting Z = h into the equation (7-3) and solving for t As shown in FIG.
t = (h-ze) / (zpp-ze)
Similarly, since the point Q (xq, yq, h) is an intersection of the “Z = h” plane and the projection line Lq, Z = h in the equation (8-3) is obtained. Substituting and solving for s, as shown in FIG.
s = (h-ze) / (zqq-ze)
The following formula (10) is obtained. Therefore, substituting X = xp, Y = yp, and t calculated in equation (9) into equations (7-1) and (7-2), respectively, and into equations (8-1) and (8-2) , X = xq, Y = yq, and substituting s obtained in equation (10), respectively, the four equations (11-1), (11-2), (11- 3) and (11-4) will be obtained. These expressions are obtained by projecting a point P (xp, yp, h) and a point Q (xq, yq, h) onto the projection plane S with the viewpoint E (xe, ye, ze) as a reference, respectively. xpp, ypp, zpp) and QQ (xqq, yqq, zqq) are obtained.

These four expressions (11-1), (11-2), (11-3), and (11-4) are conditional expressions indicating that the tangent vector T is a tangent at the point P on the structure circle C. Substituting into (6) yields equation (12) shown in FIG. 20 (f). Among the variables included in the equation (12), xpp, ypp, zpp are known quantities as the coordinate values of the point PP, xqq, yqq, zqq are known quantities as the coordinate values of the point QQ, Since xe, ye, and ze are known quantities as the coordinate values of the viewpoint E, the unknown number h can be obtained. By substituting h that has become known in this way into equations (11-1) and (11-2), xp and yp that were unknowns can be obtained. Thus, the corresponding point P (xp, yp, h) having three-dimensional coordinates can be obtained by calculation based on the point PP (αpp, βpp) having only two-dimensional coordinates. Further, the radius R of the structural circle C can be calculated using an equation R = (xp ² + yp ² ) ^{1/2 as} shown in FIG.

  After all, if an arbitrary reference point PP is defined on the contour line CCside on the projection plane S shown in FIG. 17, the corresponding point P corresponding to this is obtained by the above-described calculation. A structural circle C can be defined. Therefore, if a plurality of n reference points PP are defined on the contour line CCside at predetermined intervals, the corresponding points P are obtained for each reference point PP, and the structural circle C is defined for each corresponding point P. As shown in the perspective view of FIG. 14, a plurality of n structural circles C1 to Cn can be defined in the XYZ three-dimensional coordinate system. Furthermore, if reference circles Cbottom and Ctop obtained in the first half of §1 are added as structural circles, a total of (n + 2) structural circles can be defined. If the surface data of an object made of a rotating body is created based on a set of these structural circles and is output as three-dimensional information, the target three-dimensional object can be restored.

  In order to create surface data of an object based on a set of a large number of structural circles C, for example, as shown in FIG. The polygon structure may be defined by FIG. 21 shows an example in which a large number of squares are defined between the i-th structural circle Ci and the (i + 1) -th structural circle Ci + 1. Specifically, the circumference of each of the structural circles Ci and Ci + 1 is divided into K equal parts, and K division points (shown by black dots in the figure. The back side is omitted) are defined on the circumference and adjacent to each other. What is necessary is just to define many squares by connecting the dividing points to perform like illustration. Actually, the distance between the two adjacent structural circles and the distance between the two adjacent dividing points are set to very small values, so that the large number of squares thus obtained are all small squares, The three-dimensional object to be restored is expressed as an aggregate of these small squares.

<<< §3. Overall procedure of the present invention >>
So far, the basic principle of the three-dimensional information restoration according to the present invention has been described in the first half (§1) and the second half (§2). Here, the overall procedure of the restoration process based on this basic principle will be described.

  FIG. 22 is a flowchart showing the entire procedure of the three-dimensional information restoration process according to the present invention. It should be noted that the present invention is premised on implementation using a computer, and each step of this procedure is performed using a computer.

  First, in step S1, a two-dimensional image to be processed is input. This two-dimensional image is an image obtained by photographing an object made of a rotating body under a predetermined photographing condition. For example, a two-dimensional image including an object image 20 as shown in FIG. 2 is given as a photograph. In such a case, the image input device such as a scanner is used to process the two-dimensional image on the photograph as digital data into the storage device of the computer. Of course, when a two-dimensional image that has already been digitized is given, a process of importing it into the storage device of the computer may be performed. For example, when an image taken with a digital camera or an image that has already been digitized for plate making is given, the given digital data may be taken into the computer as it is. The two-dimensional image capture magnification may be arbitrary. This is because, as described in section 1 with reference to FIG. 10, the position of the projection surface S on the optical axis L is arbitrarily set, so that it is not necessary to consider the factor of magnification.

  The basic principle described above is based on the premise that the given two-dimensional image is a projection image obtained by projecting the three-dimensional image 10 onto a predetermined projection plane S by perspective projection as shown in FIG. The position of the perpendicular foot G (in other words, the intersection point G of the optical axis L and the projection surface S) from the viewpoint E to the projection surface S needs to be the center point of the two-dimensional image. is there. When an object is photographed using a general camera, the optical axis L is adjusted to be the center point of the photographing field of view, so the photographed two-dimensional image satisfies this condition.

  However, some digital cameras have a function of forming an image using only some of the pixels of the CCD arranged on the imaging surface in order to perform camera shake correction, and the like. It is preferable to perform correction so that the optical axis L becomes the center point of the two-dimensional image. Also, in the case of a two-dimensional image cut out by trimming after shooting, the optical axis L at the time of shooting deviates from the center point, so it is preferable to perform correction to return to the state before trimming. However, in practical use, even if the point G is slightly deviated from the center point of the two-dimensional image, a very large error does not occur. Therefore, even if such correction is not performed, no great trouble occurs.

  Further, in the embodiment shown in FIG. 1, since the upper and lower sides of the rectangle constituting the outline of the two-dimensional image are parallel to the XY plane, the object image 20 of the eyelid is arranged in the correct orientation on the image shown in FIG. Has been. Usually, when shooting an object placed on the floor, it is common to hold the camera horizontally or vertically, and if it is a two-dimensional image shot by this general method, its outline is composed. The upper and lower sides of the rectangle to be parallel are parallel to the XY plane, so that the eyelid object image 20 is in the correct orientation. However, in the case of a two-dimensional image taken with the camera held at an angle of 45 °, the eyelid object image 20 appears in an inclined state, so it is preferable to perform rotation correction in advance. However, in practice, if the object image 20 is arranged in a direction that does not cause a sense of incongruity when a two-dimensional image is observed with the naked eye, even if the position of the camera at the time of shooting is slightly tilted, a great trouble occurs. Absent.

  In the next step S2, the distance f is input. This distance f is a parameter indicating “distance between the viewpoint and the projection plane”, and is the distance between the viewpoint E and the point G in the projection system shown in FIG. As described in §1, the distance f is a parameter that governs the shape, size, and position of the object image on the projection surface S. Therefore, in the present invention, the distance f is not set as a variable parameter but is input as a fixed parameter in advance. ing. This distance f is a parameter given as one of shooting conditions at the time of shooting an object, and needs to be known information as data indicating the shooting conditions. In other words, in order to restore the three-dimensional information of the object from the two-dimensional object image according to the present invention, it is necessary to acquire information indicating the distance f in the photographing environment of the object in some form.

  As described above, when an object is photographed with a general camera, the distance f between the projection plane S and the viewpoint E is a value corresponding to the focal length of the camera, and thus the focus of the camera used at the time of photographing. If the distance data remains, information indicating the distance f remains. Further, the value input in step S2 does not necessarily need to be data indicating the distance f itself, and may be data that can indicate the distance f in some form. For example, if the information on the angle of view of the camera used at the time of photographing remains, the distance f can be calculated. Therefore, in step S2, the information on the angle of view may be input. Even if no information is left at the time of shooting, if the estimated value of the focal length f at the time of shooting can be obtained by analyzing the two-dimensional image input in step S1, It is also possible to use this estimated value as the distance f.

  In general, professional photographers often take note of shooting conditions for each photo when taking a photo. The shooting conditions that are subject to the memo usually include information such as date, lighting environment, exposure value, shutter speed, and other information such as the model of the camera used and the model number of the lens, that is, the focal length of the camera used during shooting. Is included. Therefore, commercial photographs such as ceramics published in magazines and catalogs often contain information indicating the focal length. Of course, if a photograph is taken on the premise of implementation of the present invention, information on the focal length and the angle of view of the camera used for photographing may be left intentionally. In addition, some recent digital cameras have a function of automatically recording these data together with photographed image data. When a photographed image is read out from such a digital camera, the data indicating the photographing condition is added together with the image data. Therefore, the procedure of step S1 and the procedure of step S2 are executed simultaneously. become.

  Subsequently, in step S3, processing for determining the projection plane S and the viewpoint E is performed. This is a process that should be the final purpose of the first-stage process described in §1, and has a meaning of defining a projection system necessary for performing the second-stage process described in §2. For the operator, the process of steps S1 and S2 is a simple data input process to the computer, whereas the process of step S3 is a process of repeating trial and error while viewing the image displayed on the display. become. That is, as described in detail in §1, the operator looks at the superimposed display (display in which the object image 20 and the two sets of the circular projection images CCbottom and CCtop are superimposed) as shown in FIG. The circular projection images CCbottom and CCtop are operated so as to coincide with the arcuate features 21 and 22 of the object image 20 by adjusting the setting of each parameter shown in FIG.

  Although this work is a work by trial and error, in the present invention, since the parameter called the distance f is input as a known fixed parameter, the parameters to be adjusted by the operator are as shown in FIG. , The elevation angle θ of the optical axis L, the position of the intersection ξ, the radius Rbottom, the radius Rtop, and the distance D are summarized. Moreover, it is possible to predict what changes will occur on the superimposed display when each of these parameters is changed, so the operator's parameter correction work is not a random work but a target. It is a systematic work that approaches steadily.

  Note that the coincidence between the circular projection images CCbottom and CCtop and the arcuate features 21 and 22 is not necessarily a perfect coincidence, and it is sufficient if the operator can determine that a coincidence with a predetermined accuracy is obtained. It is. The operator gives a match instruction when the match is found with a certain degree of accuracy in consideration of the resolution of the two-dimensional image input in step S1 and the accuracy required for the three-dimensional information to be restored. You just have to decide what to give.

  In the above-described embodiment, the operator gives a matching instruction by his / her own judgment, but it is also possible to leave the matching judgment to the computer. Specifically, the computer itself has a function of recognizing the arc-shaped features 21 and 22 by some pattern recognition program, and the shapes of the circular projection images CCbottom and CCtop and the arc-shaped features 21 and 22 The size and position errors may be determined quantitatively, and the coincidence determination may be made when the errors fall within a predetermined allowable range. In this case, the operator may perform the operation of correcting the parameters until the coincidence determination is made by the computer.

  In the example described in §1, the portion corresponding to the lower end surface of the object is the first arcuate feature 21 and the portion corresponding to the upper end surface of the object is the second arcuate feature 22, and FIG. As shown in FIG. 3, the circular projection images CCbottom and CCtop are matched with the positions of the upper and lower end faces of the heel. However, the arc-shaped feature portion of the object image 20 is not necessarily limited to the upper end face or the lower end face. is not. In the case of the kite illustrated in the drawings exemplified in the above-described embodiment, the arc-shaped feature portion appears remarkably on the upper end surface and the lower end surface. However, since the original three-dimensional object 10 is a rotating body, May have arcuate features at various locations. For example, an arc-shaped feature may appear in the neck portion of the neck, etc., and if the object surface has an annular pattern, it can be recognized as an arc-shaped feature. Is possible.

  Therefore, in carrying out the present invention, the arcuate feature portion that is the counterpart to match the circular projection images is not necessarily limited to the upper end surface or the lower end surface. In the above-described embodiment, an example in which two sets of circular projection images are matched with two sets of arc-shaped features is shown. However, three or more sets of circular projection images are matched with three or more sets of arc-shaped features. It doesn't matter if you do. In other words, the projection plane S and the viewpoint E cannot be uniquely determined if only one set of coincidence matching is performed, but if there are two or more sets of matching verification, the projection plane S and the viewpoint E are uniquely determined. It can be done. Eventually, in this step S3, based on the position and shape of at least two sets of arc-shaped features included in the object image on the two-dimensional image input in step S1, and the distance f input in step S2, the object The position of the optical axis L, which is one of the imaging conditions at the time of imaging, is determined, a predetermined projection plane S orthogonal to the optical axis L, and a location separated from the projection plane S by the distance f along the optical axis L It is only necessary to perform processing for determining the viewpoint E positioned at the position as the projection condition.

  However, in practice, as exemplified in the embodiment of §1, it is most preferable to perform two sets of matching verification using the upper end surface and the lower end surface of the object as arcuate features. When three or more sets of matching verification are performed, the operator's work becomes complicated, and two sets of matching verification are sufficient. In many objects, arc-shaped features tend to appear on the upper and lower end surfaces. Of course, in the case of an object with a special shape such as a cone or a sphere, the upper end surface and the lower end surface may not be a circle, but in the case of a general object such as a pottery basket or a vase, the upper end surface An arc-shaped feature appears on the lower end surface. Further, the upper end surface and the lower end surface are collation targets that are farthest apart from each other, and it is preferable to perform coincidence collation using the upper end surface and the lower end surface in order to improve the accuracy of determining the projection condition.

  The procedure of steps S1 to S3 described above corresponds to the first half process described in §1. The subsequent steps S4 and S5 are the latter-stage process described in §2.

  First, in step S4, the outline CCside is extracted. This is a process of extracting the contour line CCside on one side surface of the object image 20 included in the two-dimensional image arranged on the projection surface S as shown in FIG. The two-dimensional image to be processed in this procedure is, of course, the two-dimensional image input in step S1, and is arranged so that the center point of the image is at point G. Here, the point G is a perpendicular foot G dropped from the viewpoint E determined in step S3 to the projection plane S, and corresponds to the position of the optical axis L when the object image 20 is captured. The reason why the contour line is extracted on the projection plane S is that the extracted contour line CCside is a curve defined on the αβ two-dimensional coordinate system defined on the projection plane S. Therefore, the extracted contour line CCside is expressed as a set of points having the coordinate values (α, β).

  As described in §2, this contour extraction is performed by causing the operator to perform a trace operation for tracing the contour line in a state where an image as shown in FIG. 12 is displayed on the display. Or a process of automatically extracting a contour line on a computer based on a difference in pixel values of individual pixels constituting a two-dimensional image.

  When performing automatic extraction by a computer, if necessary, the automatically extracted contour line is corrected based on the trace operation trace by the operator, and the corrected contour line is used as a formal contour line. It is preferable to extract. For example, since a three-dimensional object 10 having a front shape as shown in FIG. 23 is photographed obliquely from above, the outline of the object image 20 with respect to the part surrounded by the alternate long and short dash line in FIG. Let's consider the case where In this case, when the computer extracts the contour line based on the difference in pixel values, the boundary line between the background portion pixel and the heel portion pixel is extracted as the contour line. CCside is as shown by the solid line in the upper right diagram. In other words, the neck portion of the heel is originally constricted. However, if the elevation angle θ at the time of photographing is large, information on the constricted portion is lost in the automatically extracted contour line CCside.

  Therefore, in such a case, correction based on the trace of the trace operation by the operator is performed. Since the object image 20 includes shading surface shading and pattern information, the operator can recognize from the information that the neck portion is originally constricted. The position of the contour line of the side surface, that is, the position indicated by the broken line in the figure can be grasped. Therefore, the trace operation along the broken line may be performed so that the corresponding section of the automatically extracted contour line CCside can be corrected to the position indicated by the broken line. The computer can perform a process of correcting the contour line CCside based on the correction input given by the operator.

  In the final step S5, a process for creating three-dimensional information is performed. This process is a process of creating three-dimensional information of the original object based on the projection plane S and viewpoint E determined in step S3 and information indicating the position of the contour line CCside extracted in step S4. it can. The basic concept of this processing is to calculate the three-dimensional information of an object such that a contour line CCside is obtained by perspective projection onto the projection plane S with the viewpoint E as a reference, taking into account the condition that the object is a rotating body It means that it asks by. Specifically, a plurality of reference points PP are defined at predetermined intervals on the contour line CCside extracted in step S4, corresponding points P corresponding to the individual reference points PP are obtained, and the structure passing through the corresponding points P A process of defining a circle C, creating surface data of an object made of a rotating body based on the set of structural circles C, and outputting the data as three-dimensional information is performed.

  Here, the relationship between one reference point PP and the corresponding point P and structural circle C corresponding thereto is “included in a predetermined plane orthogonal to the Z axis on the XYZ three-dimensional coordinate system, and on the Z axis. A structural circle C having a center point and passing through the corresponding point P is defined, a tangent vector T at the corresponding point P with respect to the structural circle C is obtained, and the tangent vector T is perspectively projected onto the projection plane S with the viewpoint E as a reference. The two-dimensional vector TT obtained on the projection surface S is a tangent to the contour line CCside at the reference point PP, and the calculation for obtaining the corresponding point P and the structural circle C from the reference point PP. Is an operation based on the above conditions. The specific method of this calculation is as already described in §2.

  In the embodiment described in §2, as shown in FIG. 21, a large number of minute squares are defined between the structural circles, and the surface information of the object is expressed by the number of minute squares. The representation format of the three-dimensional information output as the object information to be restored is not limited to such a set of minute quadrilaterals. For example, a set of minute triangles or other polygon representations may be used. . Further, as shown in FIG. 14, the aggregate of many structural circles itself is a wire frame display of a three-dimensional object, so that the aggregate of the structural circle itself is represented by the three-dimensional object to be restored. It may be output as information. Of course, it is also possible to create and output a wire frame display in which a longitudinal wire is further added to this structural circle.

<<< §4. Basic configuration of restoration apparatus according to the present invention >>
Finally, the basic configuration of the rotating body three-dimensional information restoration apparatus according to the present invention will be described with reference to the block diagram of FIG. Note that here, description will be made assuming that the constituent elements of the restoration device according to the present invention are regarded as individual functional blocks, but in reality, the restoration device shown in FIG. 24 incorporates a dedicated program into the computer. The components shown as individual blocks are elements realized by the individual functions of the program.

  As shown in the figure, this restoration apparatus is constituted by a two-dimensional image input means 100, an imaging condition input means 200, a projection condition determination means 300, a contour line extraction means 400, and a three-dimensional information creation means 500. This is a device that restores the three-dimensional information of the original object based on a two-dimensional image obtained by photographing from a predetermined direction. Here, each of the means 100 to 500 is a component for executing steps S1 to S5 in the flowchart shown in FIG.

  First, the two-dimensional image input unit 100 has a function of inputting a two-dimensional image including an object image obtained by photographing an object made of a rotating body under predetermined photographing conditions. Specifically, when a two-dimensional image is provided as a physical medium such as a photograph, the input unit 100 can be configured by a scanner device or the like. When a two-dimensional image is given as digital data, the input means 100 can be configured by a general data input device having a function of taking such digital data into a computer. Of course, digital data can also be captured online via a communication line.

  On the other hand, the photographing condition input unit 200 has a function of inputting information indicating “distance f between the viewpoint and the projection plane” given as one of photographing conditions. In general, information called photographing conditions includes various information such as illumination environment, exposure value, shutter speed, camera focal length and angle of view. The photographing conditions that need to be input by the input unit 200 are “ It is only the information indicating the distance “f” between the viewpoint and the projection plane. As described above, as the information indicating the distance f, information indicating the focal length and angle of view of the camera used for photographing can be used. When the operator manually inputs such information, for example, the input unit 200 can be configured by a general input device such as a mouse or a keyboard. Further, if such information is taken from a digital camera or the like, the input means 200 can be constituted by a general data input device having a function of taking digital data into a computer. Of course, the information indicating the distance f may be captured online via a communication line.

  Actually, when both the two-dimensional image and the information indicating the distance f are captured from the digital camera, the input means 100 and 200 are configured by the same data capturing device (device that captures information from the digital camera into the computer). Can do. As described in §3, it is not always necessary to input an accurate value at the time of photographing as the distance f, and an estimated value obtained by analyzing a two-dimensional image given to the two-dimensional image input unit 100 is used. You can use it. In this case, the imaging condition input means 200, instead of inputting the value of the distance f given from an operator, a digital camera, or the like, is estimated from an analysis device having a function of analyzing the two-dimensional image and estimating the distance f. A value may be input as the distance f.

  Thus, the two-dimensional image input by the input unit 100 and the information indicating the distance f input by the input unit 200 are given to the projection condition determination unit 300. The projection condition determining means 300 is a component having the function of executing the process of step S3 in FIG. 22, and its purpose is to determine a predetermined projection plane S and viewpoint E. The positions of the projection plane S and the viewpoint E determined here do not necessarily coincide completely with those at the time of photographing because the factors of magnification are not taken into consideration. However, except for the factors of magnification, the positions at the time of photographing are not necessarily included. The projection conditions are met.

  The basic principle of the processing performed by the projection condition determining means 300 is as described in detail in §1, and the outline of the processing is to present the screen as shown in FIG. 8 to the operator and perform the parameter correction operation to the operator. In other words, the projection plane S and the viewpoint E are determined based on the parameters set at the time when the collation target is confirmed. Specifically, the projection condition determination unit 300 includes the positions and shapes of the two sets of arc-shaped features included in the object image on the two-dimensional image given from the two-dimensional image input unit 100, and the imaging condition input unit 200. The position of the optical axis L, which is one of the imaging conditions, is determined on the basis of the distance f given from, a predetermined projection plane S orthogonal to the optical axis L, and the optical axis L from the projection plane S. And a viewpoint E positioned at a location separated by a distance f along the projection line is determined as a projection condition.

  In order to execute the processing based on such a basic principle, the projection condition determining means 300 has four configurations including a superimposing display section 310, a perspective projection calculating section 320, a parameter setting section 330, and a condition determining section 340 as shown in the figure. It has elements. The individual functions of these components will be described later.

  The contour line extracting unit 400 arranges the two-dimensional image given from the two-dimensional image input unit 100 on the projection plane S using the projection plane S and the viewpoint E thus determined by the projection condition determining unit 300. This is a component that performs processing for extracting the contour line CCside on one side surface of the object image 20 included in the two-dimensional image. At this time, the two-dimensional image is arranged so that the center point thereof coincides with the foot G of the perpendicular line that descends from the viewpoint E to the projection plane S (in other words, the intersection of the optical axis L and the projection plane S). .

  As already described, the processing performed in the contour line extraction unit 400 can be performed as processing for extracting a contour line based on the trace of the trace operation performed by the operator on the two-dimensional image. It is also possible to perform the process of automatically extracting the contour line based on the difference between the pixel values of the individual pixels constituting the two-dimensional image. In addition, as described in §3, as a process of performing the correction based on the trace of the trace operation performed by the operator on the two-dimensional image with respect to the automatically extracted outline, and extracting the corrected outline It is also possible to do this. Actually, a dedicated program for performing such processing is prepared. As a result of this processing, the contour line extraction unit 400 outputs information on the contour line CCside as indicated by a thick line in FIG.

  Note that, as in the embodiment described in §1, the “part corresponding to the lower end surface of the object” included in the object image 20 is the first arc-shaped feature 21, and “the part corresponding to the upper end surface of the object” Is the second arcuate feature 22, a contour line CCside having both points on one point on the first circular projection image CCbottom and one point on the second circular projection image CCtop is extracted. You can do that.

  Based on the projection plane S and viewpoint E determined by the projection condition determination unit 300 and the contour line CCside extracted by the contour line extraction unit 400, the three-dimensional information creation unit 500 generates a three-dimensional information of the original object. It is a component with a function to create information. In other words, on the three-dimensional coordinate system, by performing perspective projection on the projection plane S with the viewpoint E as a reference, processing for obtaining three-dimensional information of an object from which a contour line CCside can be obtained is performed. At this time, by setting the condition that the original object is a rotating body, the depth information lost on the two-dimensional image is covered.

  In order to execute the processing based on such a basic principle, the three-dimensional information creation unit 500 includes three components, that is, a reference point definition unit 510, a structural circle definition unit 520, and a surface data creation unit 530, as illustrated. I have. The individual functions of these components will be described later.

  Next, individual components shown in the projection condition determining unit 300 will be described. First, in the XYZ three-dimensional coordinate system, the parameter setting unit 330 is a parameter that defines the position of the optical axis L, and a first reference that is included in a first plane orthogonal to the Z axis and that has a center point on the Z axis. A function for setting a parameter for defining a circle and a parameter for defining a second reference circle included in a second plane perpendicular to the Z axis and having a center point on the Z axis based on an instruction from the operator. Component. Of course, since the operator performs input to correct the setting values of these parameters as needed, the parameter setting unit 330 receives an input to correct such parameter setting values and has a function of correcting the setting values. Have.

  In the example described in §1, the angle θ between the optical axis L and the XY plane and the position of the intersection ξ between the optical axis L and the XY plane are used as parameters that define the position of the optical axis L. Also, since the first reference circle Cbottom is always a circle on the XY plane and the second reference circle Ctop is a circle on the plane “Z = D”, the parameters defining each reference circle are the first The reference circle radius Rbottom, the second reference circle radius Rtop, and the value of D are used. Eventually, as shown in FIG. 11, the five parameters of θ, ξ position, Rbottom, Rtop, and D are set, and the operator sets these five parameters in the parameter setting unit 330. Instructions to do so.

  In practice, initial default values for these five parameters are set as defaults. In the first stage, the initial setting values are automatically set in the parameter setting unit 330, and are based on instructions from the operator. Thus, the value of each parameter may be corrected. For example, a superimposed display as shown in FIG. 8 is presented to the operator, and the operator sets each parameter so that the circular projection image to be collated and the arcuate feature portion coincide on the display screen. An operation for inputting an instruction to correct the image is performed.

  Here, as shown in FIG. 11, each parameter is given a role that has a specific influence on the shape, size, and position of the circular projection image. Therefore, in practice, it is preferable to present the role of each parameter to the operator. For example, a setting operation for increasing / decreasing the angle θ is presented as an operation for performing “shape correction of a circular projection image”, and for a setting operation for changing the position of the intersection ξ, What is necessary is just to show that it is operation for performing "position correction." Similarly, the setting operation for increasing / decreasing the radius Rbottom of the first reference circle and the radius Rtop of the second reference circle is presented as an operation for performing “size correction of each circle projection image”. The setting operation for increasing / decreasing the value D may be presented as an operation for performing “relative position correction of two circular projection images”.

  In practice, an operation for correcting individual parameters is to display operation knobs and dials for correcting each parameter on the display screen and allow the operator to perform an operation input for moving these parameters. Therefore, for example, the operation knob for correcting the shape of the circular projection image is presented as “Circular correction of the shape of the circular projection image”, and the operator operates the operation knob to increase or decrease the value of the parameter θ. It suffices to make such a setting correction. Similarly, the operation knob for correcting the size of the circle projection image (two sets of the circle projection image CCbottom and the circle projection image CCtop are provided) is “circle projection image size correction”. It is only necessary to make a setting correction so as to increase or decrease the values of the parameters Rbottom and Rtop by presenting and operating the operation knob by the operator. The same applies to the operation knob for changing the position of the intersection ξ and the operation knob for increasing or decreasing the value D. By using these operation knobs, the operator can correct each parameter value by an intuitive operation, and can perform an operation of matching the circular projection image with the arcuate feature portion.

  The perspective projection calculation unit 320 is a component that performs the function of calculating the circular projection images CCbottom and CCtop based on the values of the parameters currently set in the parameter setting unit 330. In practice, a predetermined algorithm Is a component realized by a program that executes such an operation. In the case of the above-described embodiment, the five parameters such as θ, ξ position, Rbottom, Rtop, and D set in the parameter setting unit 330 are as follows. This is information indicating the position of the second reference circle Ctop.

  Therefore, the perspective projection calculation unit 320 first defines a predetermined projection plane S orthogonal to the optical axis L on the XYZ three-dimensional coordinate system. As already described, since the magnification factor does not need to be considered in the present invention, the projection plane S may be defined at any position as long as it is a plane orthogonal to the optical axis L. Therefore, for example, a predetermined distance d may be determined in advance, and a process of defining the projection plane S at a position separated from the intersection ξ by the distance d may be performed. Further, since the value of the distance f is given from the photographing condition input means 200, the viewpoint E can be uniquely defined at a place away from the projection plane S along the optical axis L by the distance f.

  Further, since the perspective projection calculation unit 320 is provided with information indicating the position of the first reference circle Cbottom and the position of the second reference circle Ctop, the first reference circle Cbottom and the second reference circle Ctop are It is possible to perform an operation of performing perspective projection on the projection surface S with the viewpoint E as a reference, and obtaining the first circle projection image CCbottom and the second circle projection image CCtop on the projection surface S.

  Thus, the information indicating the positions of the projection plane S and the viewpoint E obtained by the perspective projection calculation unit 320 and the information indicating the shapes and positions of the first circular projection image CCbottom and the second circular projection image CCtop are superimposed and displayed. To the unit 310. The superimposed display unit 310 arranges the two-dimensional image given from the two-dimensional image input means 100 on the projection plane S, and the first circle projection image Cbottom and the second circle projection image Ctop are placed on the two-dimensional image. Is a component having a function of displaying a state in which is superimposed on the display screen. At this time, the two-dimensional image is arranged so that its center point coincides with the foot G of the perpendicular line drawn from the viewpoint E to the projection plane S.

  Of course, if the operator gives an instruction to the parameter setting unit 330 to correct the parameter value, the parameter setting value in the parameter setting unit 330 changes, and the calculation result by the perspective projection calculation unit 320 also changes. As a result, the display content of the superimposed display unit 310 also changes. The operator observes the display result (for example, the display result as shown in FIG. 8) by the superimposed display unit 310 output on the display screen, and the first circular projection image CCbottom and the first arcuate feature unit 21. So that the second circular projection image CCbottom and the second arcuate feature portion 21 coincide with each other, and a parameter correction instruction is given to the parameter setting unit 330. Will be reflected on the display screen.

  In the display by the superimposition display unit 310, the condition determination unit 340 matches the first arcuate feature 21 of the object image with all or a part of the first circular projection image CCbottom with a predetermined accuracy. When the operator gives a coincidence instruction indicating that the second arcuate feature 22 and the whole or a part of the second circular projection image CCtop coincide with each other with a predetermined accuracy, the perspective projection calculation unit 320 at that time. Fulfills the function of determining the projection plane S and the viewpoint E defined by H. as the projection plane S and the viewpoint E as final projection conditions. For example, when a matching state as shown in FIG. 12 is obtained on the display screen, the operator may perform an operation for giving a matching instruction to the condition determining unit 340.

  Thus, when a coincidence instruction is given from the operator, information indicating the projection plane S and the viewpoint E (for example, the plane expression indicating the projection plane S and the viewpoint E on the XYZ three-dimensional coordinate system) is received from the condition determination unit 340. Coordinate value) is given as an output of the projection condition determining means 300. Note that, as described in §3, the first arc-shaped feature portion and the second arc-shaped feature portion of the object image do not necessarily correspond to “the portion corresponding to the lower end surface of the object” and “the upper end surface of the object. It is not necessary to use “parts”, and it is left to the operator to decide which part is the arcuate feature to be matched. Further, as described in §4, instead of leaving the match determination to the operator, the match determination may be automatically performed by a predetermined algorithm. In this case, the condition determination unit 340 performs the matching determination by its own determination, and therefore it is not necessary to input a matching instruction from the operator.

  Finally, the individual components shown in the three-dimensional information creation unit 500 will be described. First, the reference point definition unit 510 is a component that performs a function of defining a plurality of n reference points PP at predetermined intervals on the contour line CCside extracted by the contour line extraction unit 400. Here, the value of n is a value that influences the resolution of the finally obtained three-dimensional restored image. Therefore, when it is desired to obtain a restored image with a high resolution, the value of n may be set large. The interval between the reference points PP may be arbitrarily set. For example, if the total length of the contour line CCside is equally divided into (n + 1) and each equal dividing point is set as the reference point PP, a total of n reference points PP1 to PP1. PPn can be obtained. In the case of the embodiment described in §2, each reference point PP is defined as a point on the αβ two-dimensional coordinate system, and thus has a two-dimensional coordinate value of (αpp, βpp). As described above, by performing coordinate conversion in consideration of the position of the projection plane S defined on the XYZ three-dimensional coordinate system, the point is converted into a point having a three-dimensional coordinate value of (xpp, ypp, zpp).

  As shown in FIG. 17, the structural circle definition unit 520 is a component that calculates a corresponding point P corresponding to the reference point PP and performs an operation to define a structural circle C that passes through the corresponding point P. As described above, since the reference point defining unit 510 defines a plurality of n reference points PP1 to PPn, the structural circle defining unit 520 defines a plurality of n structural circles C1 to Cn. . The calculation for obtaining the structural circle C from the reference point PP is as follows: “In the XYZ three-dimensional coordinate system, a structural circle C included in a predetermined plane orthogonal to the Z axis, having a center point on the Z axis, and passing through the corresponding point P A two-dimensional vector TT obtained on the projection plane S is obtained by obtaining a tangent vector T at the corresponding point P with respect to the structural circle C, and perspectively projecting the tangent vector T onto the projection plane S with the viewpoint E as a reference. , Which is a tangent to the contour line CCside at the reference point PP ”.

  Specific arithmetic expressions are as shown in FIGS. This operation is eventually summarized as follows. First, as shown in FIG. 17, the coordinate value (xp, yp, h) of the corresponding point P and the coordinate value (xq, yq, h) of the tip point Q on the XYZ three-dimensional coordinate system are defined as unknowns.

  On the other hand, on the projection surface S, reference points PP (αpp, βpp) are defined. The coordinate values (αpp, βpp) of the reference point PP are coordinate values given from the reference point definition unit 510 and are known values. Further, since the tangent line of the contour line CCside can be defined at the reference point PP, the tangent vector TT is defined on the tangent line. The tangent vector TT can be defined by determining the position of the tip point QQ on the projection plane S. Here, since the length of the vector TT may be arbitrary, the tip point QQ can be defined as an arbitrary point on the tangent line of the contour line CCside at the reference point PP. The coordinate values (αqq, βqq) are known values.

  Next, the known coordinate values (αpp, βpp) of the reference point PP and the known coordinate values (αqq, βqq) of the tip point QQ on the αβ two-dimensional coordinate system defined on the projection plane S are converted into an XYZ three-dimensional coordinate system. By using the position information of the projection plane S on the upper side, calculations for converting into coordinate values (xpp, ypp, zpp) and (xqq, yqq, zqq) on the XYZ three-dimensional coordinate system are performed. Naturally, the coordinate values xpp, ypp, zpp, xqq, yqq, zqq are known values.

Subsequently, when a conditional expression indicating that the tangent vector T is a tangent at the corresponding point P of the structural circle C is obtained, the following expression (6) is obtained as shown in FIG.
-Xp / yp = (yq-yp) / (xq-xp) (6)

On the other hand, the reference point PP and the tip point QQ perspective-project the corresponding point P and the tip point Q onto the projection plane S with the viewpoint E whose position is defined by the known coordinate values (xe, ye, ze) as a reference. When the conditional expression indicating that the point is obtained by this is obtained, the following four expressions are obtained as shown in FIG.
xp = ((h-ze). (xpp-xe)) / (zpp-ze) + xe (11-1)
yp = ((h-ze). (ypp-ye)) / (zpp-ze) + ye (11-2)
xq = ((h-ze). (xqq-xe)) / (zqq-ze) + xe (11-3)
yq = ((h-ze). (yqq-ye)) / (zqq-ze) + ye (11-4)

Therefore, by substituting these four equations into equation (6), as shown in FIG. 20, equation (12) containing only h as an unknown is obtained. By solving this equation, the value of unknown h is obtained. Can be calculated. Then, by substituting the calculated value of h into the above formulas (11-1) and (11-2), the unknown coordinate values xp, yp can be obtained, and on the “Z = h” plane. , A structure circle C having a radius R = (xp ² + yp ² ) ^1/2 can be defined.

  In addition to the plurality of n structural circles C1 to Cn defined in the above-described procedure, the structural circle defining unit 520 uses the parameters set in the parameter setting unit 330 when a matching instruction is given from the operator. It is also possible to define the first reference circle Cbottom and the second reference circle Ctop to be defined as a part of the structure circle, and to define a total of (n + 2) structure circles. In this case, as shown in FIG. 14, in addition to the structural circles C1 to Cn, the restored object is represented by the reference circle Cbottom and the reference circle Ctop.

  The final surface data creation unit 530 is a component having a function of creating surface data of an object made of a rotating body based on the set of structural circles C thus obtained and outputting this as 3D information. . Specifically, for example, the surface data of the three-dimensional object to be restored may be expressed by a large number of polygons by a technique as shown in FIG. Of course, as described in §3, it is also possible to output three-dimensional information as wireframe data.

FIG. 3 is a perspective view showing a geometric relationship between a two-dimensional image and a three-dimensional object when a two-dimensional image is obtained by photographing the three-dimensional object from a predetermined direction. It is a top view of the projection surface S shown in FIG. It is a front view of the projection system shown in FIG. 1 is a perspective view of a three-dimensional object 10 having a ridge shape with a Z axis as a rotation axis. FIG. 3 is a perspective view showing a circle projection image C ′ obtained by parallel projecting a circle C on an XYZ three-dimensional coordinate system onto a projection plane S. FIG. 3 is a perspective view showing a circular projection image CC obtained by perspectively projecting a circle C on an XYZ three-dimensional coordinate system onto a projection plane S. FIG. It is a front view of the projection system for showing the basic principle of the method of determining the position of projection plane S and viewpoint E by the present invention. It is a top view which shows the state which superimposed and displayed the imaged two-dimensional image and circular projection image CCbottom, CCtop on the projection surface S shown by FIG. FIG. 8 is a top view of the projection system shown in FIG. 7. It is a front view of the projection system explaining the influence which the position of the projection surface S on the optical axis L has on the projection image. It is the figure which arranged and showed the influence which five parameters in the projection system shown in Drawing 7 have on circular projection images CCbottom and CCtop. 8 shows a state in which the circular projection images CCbottom and CCtop are made to match the respective arc-shaped feature portions 21 and 22 by correcting the set values of the five parameters shown in FIG. 11 with respect to the superimposed display shown in FIG. It is a top view. It is a top view which shows the state which extracted the contour line CCside of the left side surface about the object image 20 displayed on the projection surface S. FIG. It is a perspective view which shows the state which decompress | restores three-dimensional information by defining many structural circles C1, C2, C3, ..., Ci, ..., Cn. It is a perspective view which shows the structure circle C defined on the surface of the object 10 on an XYZ three-dimensional coordinate system, and its tangent vector T. FIG. FIG. 16 is a plan view showing a projection image of the object 10 and the tangent vector T shown in FIG. 15 on a projection plane S. FIG. 17 is a perspective view showing a positional relationship between the three-dimensional tangent vector T shown in FIG. 15 and the two-dimensional tangent vector TT shown in FIG. 16. FIG. 18 is a first mathematical formula explanatory diagram for explaining the principle of calculation for obtaining a point P based on the point PP shown in FIG. 17. FIG. 18 is a second mathematical expression explanatory diagram for explaining the principle of calculation for obtaining a point P based on the point PP shown in FIG. 17. FIG. 18 is a third mathematical formula explanatory diagram for explaining the principle of calculation for obtaining a point P based on the point PP shown in FIG. 17. It is a perspective view which shows an example of the method of producing the surface data of a restored object based on the collection of many structural circles. It is a flowchart which shows the whole procedure of the three-dimensional information restoration process which concerns on this invention. It is a figure which shows the concept which performs the correction process by manual operation with respect to the outline CCside extracted automatically. It is a block diagram which shows the basic composition of the three-dimensional information restoration apparatus of the rotary body which concerns on this invention.

Explanation of symbols

10 ... Three-dimensional object (壺)
20 ... Object image (projection image of cocoon)
21 ... 1st circular-arc-shaped characteristic part (part corresponding to the lower end surface of an object)
22 ... 2nd circular-arc-shaped characteristic part (part corresponding to the upper end surface of an object)
DESCRIPTION OF SYMBOLS 100 ... Two-dimensional image input means 200 ... Imaging condition input means 300 ... Projection condition determination means 310 ... Superimposition display part 320 ... Perspective projection calculation part 330 ... Parameter setting part 340 ... Condition determination part 400 ... Contour line extraction means 500 ... Three-dimensional Information creation means 510 ... reference point definition unit 520 ... structural circle definition unit 530 ... surface data creation unit C ... circle on the XYZ three-dimensional coordinate system / structural circle Cbottom ... contour circle on the lower end surface of the bowl / first reference circle Ctop ... the contour circle of the top surface of the eyelid / second reference circle Cside ... the line C 'on the object corresponding to the contour CCside ... the projection image CC obtained by parallel projection of the circle C ... the perspective projection of the circle C Projected image CCbottom obtained by the following: first circular projected image CCtop second curved projected image CCside contour lines C1, C2, C3,..., Ci,. Structure circle D Distance G, G '... arrangement position of the foot h ... structure circle C of a perpendicular line which beat the projection plane from the viewpoint of the distance E ... viewpoint f ... viewpoint of both the reference circle and the projection surface (height)
L, Ly, Lw ... optical axes Lp, Lq ... projection line M ... arbitrary point O on two-dimensional image ... origin P of XYZ three-dimensional coordinate system ... corresponding point PP corresponding to reference point PP ... on contour line CCside Defined reference point Q ... tip point QQ of tangent vector T ... tip point R of tangent vector TT ... radius Rbottom of structural circle C ... radius Rtop of first reference circle Cbottom ... radius R1, second reference circle Ctop R2, R3, ..., Ri, ..., Rn ... radius S, Sy, Sw, S '... projection planes S1 to S5 ... steps T of the flow chart ... third order defined at point P on the structure circle C Original tangent vector TT ... Two-dimensional tangent vector U1, U2 defined at reference point PP on contour CCside ... Diagonal point V of two-dimensional image ... Vector indicating projection direction W ... Arbitrary axes X and Y on XY plane , Z ... coordinate axes xe, ye, ze ... coordinate value xp of viewpoint E in the three-dimensional coordinate system yp ... coordinate value xq, yq of corresponding point P ... coordinate value xpp, ypp, zpp of tip point Q ... coordinate value xqq, yqq, zqq of reference point PP on XYZ three-dimensional coordinate system XYZ three-dimensional of tip point QQ Coordinate values α, β on the coordinate system, each coordinate axis αm, βm, coordinate value αpp, βpp of the two-dimensional coordinate system defined on the projection plane S, coordinates on the αβ two-dimensional coordinate system of the reference point PP Values αqq, βqq: Coordinate value of tip point QQ on αβ two-dimensional coordinate system θ: Elevation angle of optical axis L ξ: Intersection φ between optical axis L and XY plane φ: Rotation angle of optical axis L

Claims (20)

A restoration device that restores three-dimensional information of an original object based on a two-dimensional image obtained by photographing an object made of a rotating body from a predetermined direction,
Two-dimensional image input means for inputting a two-dimensional image including an object image obtained by photographing an object made of a rotating body under predetermined photographing conditions;
Shooting condition input means for inputting information indicating “distance f between viewpoint and projection plane” given as one of the shooting conditions;
Based on the position and shape of the two sets of arc-shaped features included in the object image on the two-dimensional image and the distance f, the position of the optical axis L that is one of the imaging conditions is determined, Projection condition determining means for determining a predetermined projection plane S orthogonal to the optical axis L and a viewpoint E positioned at a distance f from the projection plane S along the optical axis L by the distance f. When,
One side of the object image in a state where the two-dimensional image is arranged on the projection plane S so that the center point of the two-dimensional image coincides with the foot G of the perpendicular line drawn from the viewpoint E to the projection plane S. Contour extracting means for extracting a side contour CCside;
Based on the information indicating the positions of the projection plane S, the viewpoint E, and the contour line CCside in a three-dimensional coordinate system, the contour line CCside is obtained by performing perspective projection on the projection plane S with the viewpoint E as a reference. 3D information creating means for creating such 3D information of an object by considering the condition that the object is a rotating body,
A three-dimensional information restoring apparatus for a rotating body, comprising: The three-dimensional information restoration apparatus according to claim 1,
Projection condition determination means
In the XYZ three-dimensional coordinate system, a parameter that defines the position of the optical axis L, a parameter that defines a first reference circle that is included in a first plane orthogonal to the Z axis and that has a center point on the Z axis, and Z A parameter setting unit that sets a parameter that defines a second reference circle that is included in a second plane orthogonal to the axis and that has a center point on the Z axis, based on an instruction from the operator;
On the XYZ three-dimensional coordinate system, a predetermined projection plane S orthogonal to the optical axis L, and a viewpoint E located at a position separated from the projection plane S along the optical axis L by the distance f. The first reference circle and the second reference circle are perspectively projected onto the projection plane S with the viewpoint E as a reference, and the first circle projection image and the second circle are projected onto the projection plane S. A perspective projection calculation unit for obtaining a projection image;
The two-dimensional image is arranged on the projection plane S so that the center point of the two-dimensional image coincides with a foot G of a perpendicular line drawn from the viewpoint E to the projection plane S, and the two-dimensional image is placed on the two-dimensional image. A superimposed display unit that displays a superimposed state of the first circular projection image and the second circular projection image on a display screen;
In the display by the superimposed display unit, the first arc-shaped feature portion of the object image and all or a part of the first circular projection image coincide with each other with a predetermined accuracy, and the second arc-shaped feature portion of the object image Projecting the projection plane S and the viewpoint E defined by the perspective projection calculation unit when a match confirmation indicating that all or a part of the second circular projection image matches with a predetermined accuracy is obtained. A condition determining unit for determining a projection plane S and a viewpoint E as conditions;
A three-dimensional information restoration apparatus for a rotating body characterized by comprising: The three-dimensional information restoration apparatus according to claim 1,
Three-dimensional information creation means
A reference point defining unit for defining a plurality of n reference points PP at predetermined intervals on the contour line CCside extracted by the contour line extracting means;
Corresponding points P corresponding to the respective reference points PP are defined as “a structural circle C included in a predetermined plane orthogonal to the Z axis on the XYZ three-dimensional coordinate system, having a center point on the Z axis, and passing through the corresponding point P. A two-dimensional vector TT obtained on the projection plane S is obtained by obtaining a tangent vector T at the corresponding point P with respect to the structural circle C, and perspectively projecting the tangent vector T onto the projection plane S with the viewpoint E as a reference. , A tangent of the contour line CCside at the reference point PP ”, a structural circle definition part that defines a plurality of n structural circles C,
Based on the set of structural circles C, create surface data of an object made of a rotating body, and output this as three-dimensional information;
A three-dimensional information restoration apparatus for a rotating body characterized by comprising: The three-dimensional information restoration apparatus according to claim 1,
Projection condition determination means
In the XYZ three-dimensional coordinate system, a parameter that defines the position of the optical axis L, a parameter that defines a first reference circle that is included in a first plane orthogonal to the Z axis and that has a center point on the Z axis, and Z A parameter setting unit that sets a parameter that defines a second reference circle that is included in a second plane orthogonal to the axis and that has a center point on the Z axis, based on an instruction from the operator;
On the XYZ three-dimensional coordinate system, a predetermined projection plane S orthogonal to the optical axis L, and a viewpoint E located at a position separated from the projection plane S along the optical axis L by the distance f. The first reference circle and the second reference circle are perspectively projected onto the projection plane S with the viewpoint E as a reference, and the first circle projection image and the second circle are projected onto the projection plane S. A perspective projection calculation unit for obtaining a projection image;
The two-dimensional image is arranged on the projection plane S so that the center point of the two-dimensional image coincides with a foot G of a perpendicular line drawn from the viewpoint E to the projection plane S, and the two-dimensional image is placed on the two-dimensional image. A superimposed display unit that displays a superimposed state of the first circular projection image and the second circular projection image on a display screen;
In the display by the superimposed display unit, the first arc-shaped feature portion of the object image and all or a part of the first circular projection image coincide with each other with a predetermined accuracy, and the second arc-shaped feature portion of the object image Projecting the projection plane S and the viewpoint E defined by the perspective projection calculation unit when a match confirmation indicating that all or a part of the second circular projection image matches with a predetermined accuracy is obtained. A condition determining unit for determining a projection plane S and a viewpoint E as conditions;
Have
Three-dimensional information creation means
A reference point defining unit for defining a plurality of n reference points PP at predetermined intervals on the contour line CCside extracted by the contour line extracting means;
Corresponding points P corresponding to the respective reference points PP are defined as “a structural circle C included in a predetermined plane orthogonal to the Z axis on the XYZ three-dimensional coordinate system, having a center point on the Z axis, and passing through the corresponding point P. A two-dimensional vector TT obtained on the projection plane S is obtained by obtaining a tangent vector T at the corresponding point P with respect to the structural circle C, and perspectively projecting the tangent vector T onto the projection plane S with the viewpoint E as a reference. , A tangent of the contour line CCside at the reference point PP ”, a structural circle definition part that defines a plurality of n structural circles C,
Based on the set of structural circles C, create surface data of an object made of a rotating body, and output this as three-dimensional information;
A three-dimensional information restoration apparatus for a rotating body characterized by comprising: In the three-dimensional information restoration apparatus according to any one of claims 1 to 4,
A three-dimensional information restoration apparatus for a rotating body, wherein the photographing condition input means inputs the focal length of the camera used for photographing as information indicating "distance f between the viewpoint and the projection plane". In the three-dimensional information restoration apparatus according to any one of claims 1 to 4,
A three-dimensional information restoration apparatus for a rotating body, wherein the photographing condition input means inputs the angle of view of the camera used for photographing as information indicating "distance f between viewpoint and projection plane". In the three-dimensional information restoration apparatus according to any one of claims 1 to 4,
The projection condition determining means uses the “part corresponding to the lower end surface of the object” and the “part corresponding to the upper end surface of the object” included in the object image as arcuate features, respectively. Original information restoration device. In the three-dimensional information restoration apparatus according to any one of claims 1 to 4,
A three-dimensional information restoration apparatus for a rotating body, wherein the contour extraction means performs a process of extracting a contour based on a trace operation trace performed by an operator performed on a two-dimensional image. In the three-dimensional information restoration apparatus according to any one of claims 1 to 4,
A three-dimensional information restoration apparatus for a rotating body, wherein the contour extraction means performs a process of automatically extracting a contour based on a difference between pixel values of individual pixels constituting a two-dimensional image. The three-dimensional information restoration device according to claim 9,
A tertiary body of a rotating body characterized in that the automatically extracted contour line is subjected to correction based on the trace operation trace performed by the operator on the two-dimensional image, and the corrected contour line is extracted. Original information restoration device. The three-dimensional information restoration apparatus according to claim 2 or 4,
The parameter setting unit uses the angle θ formed between the optical axis L and the XY plane and the position of the intersection ξ between the optical axis L and the XY plane as parameters defining the optical axis L. Original information restoration device. The three-dimensional information restoration apparatus according to claim 11,
The parameter setting unit presents that the setting operation for increasing / decreasing the angle θ is an operation for performing “shape correction of the circular projection image”, and the setting operation for changing the position of the intersection ξ “the position of the circular projection image” A three-dimensional information restoration apparatus for a rotator, which presents that the operation is for performing “correction”. The three-dimensional information restoration apparatus according to claim 2 or 4,
The parameter setting unit always sets the first reference circle as a circle on the XY plane, sets the second reference circle as a circle on the plane “Z = D”, and sets each reference circle as a parameter. And a radius of the second reference circle, and a value of D are used. The three-dimensional information restoration apparatus according to claim 13,
The parameter setting unit presents that the setting operation for increasing or decreasing the radius of the first reference circle and the radius of the second reference circle is an operation for performing “size correction of the circular projection image”, and sets the value D to A three-dimensional information restoration apparatus for a rotating body, which presents that the setting operation to increase / decrease is an operation for performing “relative position correction of two circular projection images”. The three-dimensional information restoration apparatus according to claim 13 or 14,
The “part corresponding to the lower end surface of the object” included in the object image is the first arc-shaped feature, and the “part corresponding to the upper end surface of the object” included in the object image is the second arc-shaped feature. A three-dimensional information restoration apparatus for a rotating body. The three-dimensional information restoration apparatus according to claim 15,
The contour extraction means extracts a contour CCside having both ends of one point on the first circle projection image and one point on the second circle projection image, and the three-dimensional information of the rotating body Restore device. The three-dimensional information restoration apparatus according to claim 3 or 4,
The structural circle definition part
The tangent vector TT of the contour line CCside at the reference point PP is defined as a line segment on the projection plane S connecting the two points PP / QQ by defining the tip point QQ, and the tangent vector of the structural circle C at the corresponding point P T is defined as a line segment on an XYZ three-dimensional coordinate system connecting two points P / Q by defining the tip point Q.
Using the condition that “the points obtained by perspective projection of the corresponding point P and the tip point Q onto the projection plane S with the viewpoint E as a reference coincide with the reference point PP and the tip point QQ, respectively”. A three-dimensional information restoration apparatus for a rotating body, which performs a calculation for obtaining a coordinate value of the corresponding point P on an XYZ three-dimensional coordinate system. The three-dimensional information restoration device according to claim 17,
The structural circle definition part
Define the coordinate value (xp, yp, h) of the corresponding point P and the coordinate value (xq, yq, h) of the tip point Q on the XYZ three-dimensional coordinate system as unknowns,
Projecting the known coordinate values (αpp, βpp) of the reference point PP and the known coordinate values (αqq, βqq) of the tip point QQ on the XYZ three-dimensional coordinate system defined on the αβ two-dimensional coordinate system defined on the projection plane S By using the position information of the surface S, an operation for converting into coordinate values (xpp, ypp, zpp) and (xqq, yqq, zqq) on the XYZ three-dimensional coordinate system is performed,
The first conditional expression −xp / yp = (yq−yp) / (xq−xp) indicating that the tangent vector T is a tangent at the corresponding point P of the structural circle C
The reference point PP and the tip point QQ are obtained by perspectively projecting the corresponding point P and the tip point Q onto the projection plane S with the viewpoint E defined by the known coordinate values (xe, ye, ze) as a reference. Xp = ((h−ze) · (xpp−xe)) / (zpp−ze) + xe
yp = ((h-ze). (ypp-ye)) / (zpp-ze) + ye
xq = ((h-ze). (xqq-xe)) / (zqq-ze) + xe
yq = ((h-ze). (yqq-ye)) / (zqq-ze) + ye
And the value of the unknown h is calculated by solving the obtained equation, and the calculated value of h is substituted into the second conditional expression to obtain the coordinate values xp and yp, and “Z = h A three-dimensional information restoration apparatus for a rotating body, characterized by defining a structural circle C having a radius R = (xp ² + yp ² ) ^1/2 on a plane. The three-dimensional information restoration apparatus according to claim 4,
The structural circle definition unit defines the first reference circle and the second reference circle defined by the parameters set in the parameter setting unit at the time when the coincidence confirmation is obtained as a part of the structural circle, and the total A rotating body three-dimensional information restoration apparatus characterized by defining (n + 2) structural circles.   A computer program for causing a computer to function as the three-dimensional information restoration apparatus for a rotating body according to any one of claims 1 to 19.