JPH07296184A - Center projecting method - Google Patents

Abstract

PURPOSE:To reduce distortion around an image although the more a distance between a viewpoint and a projected plane is reduced, the more the distortion around the projected image is enlarged when a projecting object is projected by a general-purpose center projecting method concerning the center projecting method for projecting the projecting object on the projected plane by emitting a beam from the view point in the shape of a cone. CONSTITUTION:After or when the projecting object is projected onto the projected plane composed of a plane, the distortion is corrected by projecting it again onto the projected plane by eyeball conversion. In this case, the eyeball conversion is the reprojection onto the projected plane through the projection onto a projected plane (projected spherical plane) defining a semispherical plane farther from the view point as this projected plane among the two semispherical planes provided by bisecting a spherical plane, which is provided with a center on a line of sight, orthogonally to the line of sight at that center position after or when the projecting object is projected onto the projected plane.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to computer graphics, and more particularly to improvement of a central projection method.

[0002]

2. Description of the Related Art The central projection method is a method of projecting a projection target on a projection surface 4 by emitting a light beam in a conical shape from a point (viewpoint) e as shown in FIG. This method is applied to the projection of a tomographic image and is used to construct a three-dimensional image (for example, Japanese Patent Application No. 6-3492).

By the way, conventionally, the projection plane in the above-described central projection method (general central projection method) is "Computer Graphix" (JD FOLEY &
A. Written by VAN DAM Translated by Atsumi Imamiya July 1, 1984
It was flat as you can see on pages 275-316 of the 5th Japan Computer Association).

[0004]

As described above, in the prior art, the projection surface in the central projection method is a plane. Therefore, the following distortion was generated. In FIG. 9B, when the projection targets 40a and 40b are projected on the projection surface 4,
It becomes projected images 40A and 40B, respectively. Projection target 40a
If the projection target 40b has the same length (the size in the left-right direction in the drawing), the projection target 40b will be viewed obliquely, and therefore should appear shorter than the projection target 40a.

However, as can be seen from FIG. 9 (b), this is not the case (longer conversely), and such distortion depending on the projection direction is caused by the distance between the viewpoint e and the projection surface 4. There was a problem that the smaller the size, the larger the size.

An object of the present invention is to provide a central projection method capable of eliminating distortion of a projected image depending on the projection direction.

[0007]

The above object is to provide a central projection method of projecting a projection object onto a projection surface by emitting light rays in a conical shape from a viewpoint, and projecting the projection object onto a projection surface composed of a plane. This is accomplished by reprojecting onto the projection plane consisting of the plane by eyeball conversion after or at the time of projection.

[0008]

8A shows the eyeball, and the light ray 7 passes through the crystalline lens (lens) 6 to form an image on the spherical retina 5. In this way, in the natural world, the retina 5 is made spherical to eliminate the distortion depending on the projection direction.

In the method of the present invention, the projection surface is a hemispherical surface as shown in FIG. 8B (see projection spherical surface 3). As a result, the distortion of the projected image depending on the projection direction is corrected, and the projection data (length or size) depends on the difference in the projection direction.
It is designed so that it does not differ.

[0010]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 is a flowchart showing an embodiment of the center projection method according to the present invention. As shown in FIG. 1, according to the center projection method of the present invention, a projection target is first formed by a general center projection method as a projection plane (primary projection plane:
Projection is performed on a projection plane before distortion correction by eyeball conversion described later, that is, a projection plane of a conventional method) (step 1).

After or at the time of projection, the projection image of the projection target is obtained by re-projecting onto the projection plane (secondary projection plane: projection plane after distortion correction by the below-mentioned eye transformation) by the below-mentioned eye transformation. (Step 2).

The term “eyeball conversion” as used herein means two values obtained by dividing a spherical surface having a center on the line of sight into two in the direction orthogonal to the line of sight after or at the time of projecting the projection target onto the projection plane. Of the hemispheres, it means reprojection onto the projection plane through projection onto the projection plane (projection sphere) whose projection surface is the hemisphere on the side far from the viewpoint.

That is, according to the present invention, the projection sphere is centrally projected as the projection surface, and in this case, each point (address) along the hemisphere which is the projection surface becomes a display pixel (address) of the CRT. Correspond. Then, in order to obtain the same effect as that projected on the projection spherical surface on a plane (CRT screen), eyeball conversion is performed and distortion correction is performed.

The principle of distortion correction by eyeball conversion of the method of the present invention will be described below with reference to FIGS. 2 and 3.
First, referring to FIG. 2, in FIG. 2, the viewpoint e is h = 2.
It shows the case of R. In FIG. 2, 3
Of two hemispheres I and II obtained by dividing a spherical surface having a center on the line of sight (Z axis) in the direction orthogonal to the line of sight at the center position, the hemisphere (hemisphere I ) Is a projection surface (hereinafter referred to as a projection spherical surface).
Further, 4 is a projection plane formed of a plane (hereinafter referred to as a projection plane), which is also a projection plane before distortion correction by eyeball conversion, that is, a primary projection plane as a projection plane of a conventional method, and after distortion correction by eyeball conversion. It is also a secondary projection plane as a projection plane of. The projection plane 4 corresponds to the screen that is the display surface of the CRT.

X, Y, Z are each axis of the three-dimensional coordinate system,
O is the origin of the three-dimensional coordinate system, e is the viewpoint, h is the distance between the viewpoint e and the projection plane 4, R is the radius of the projection sphere 3, P is a point (X1, Y1) on the projection plane 4, and ψ is a straight line. An angle formed by OP and the X axis, Q is a point on the projection spherical surface 3 corresponding to a point P on the projection plane 4 (an intersection of the straight line Pe and the projection spherical surface 3), θ is an angle formed by the straight line Z1 Q and the Z axis, L is an arc OQ on the projection sphere 3, L'is L
Is a line segment on the straight line OP having the same length as, η is a CRT display address (taken in parallel with the X axis), and ξ is a CRT display address (taken in parallel with the Y axis).

According to this, the following equation holds. When h = 2 · R corresponding to the eyeball, tan (θ / 2) = sqrt (X
For the 1 ² + Y1 ² ) / 2R triangle X1 OP, tan (ψ) = Y1 / X1 is given.

Therefore, when X1 and Y1 are specified, the corresponding η1 and ξ1 are obtained by using ψ = arctan (Y1 / X1) θ = 2 · arctan [sqrt (X1 ² + Y1 ² ) / 2R] L = R · θ Then, η1 = L · cos (ψ) ξ1 = L · sin (ψ).

These η1 and ξ1 are pixel addresses on the display memory. That is, the point (X1, Y1) on the projection plane 4 is displayed at the point (η1, ξ1) on the CRT screen, which means that the distortion correction by the eyeball conversion is performed.

Further, the image size is reduced by this eyeball conversion (point P is reduced to point (η1, ξ1)). Therefore, the image size of the projection image on the projection plane 4 after distortion correction is
It becomes possible to project larger than the image size of the image projected after being corrected by the eyeball conversion.

Next, the case where the viewpoint e is other than h = 2R will be described with reference to FIG. In FIGS. 3A and 3B, the same reference numerals as those in FIG. 2 indicate the same or corresponding portions. Also,
U is the length of the straight line eQ, γ is the angle between the line segment eP and the Z axis,
w is the length of a straight line drawn from Q perpendicular to the Z axis.

According to this, the following equation holds. U = sqrt [(h−R) ² + R ² −2 · (h−R) · R · c
os (π−θ)], U · sinγ = R · sin θ.

Γ is given by tan γ = sqrt (X1 ² + Y1 ² ) / h. From this, when X1 and Y1 are specified, θ can be obtained.

Ψ is L when calculated from tan ψ = Y1 / X1
= R · θ, η1 = L · cosψ ξ1 = L · sinψ.

These η1 and ξ1 are pixel addresses on the display memory. That is, the point (X1, Y1) on the projection plane 4 is displayed at the point (η1, ξ1) on the CRT screen, which means that the distortion correction by the eyeball conversion is performed.

The projection target may be data input by an input device such as a mouse, or the result of calculation by a calculation device such as a tomographic image (including a tomographic image obtained by decomposing a volume image by three-dimensional measurement). Data may be used.

4 to 6 show a method of constructing a three-dimensional image from a plurality of tomographic images by a general center projection method (Japanese Patent Application No. 6-3492), even in such a case, As long as projection is performed, eyeball conversion is necessary to eliminate distortion, and an example of applying the method of the present invention to a method of constructing a three-dimensional image will be described below. In both cases of FIG. 5 and FIG. 6, it is necessary to first project a tomographic image on an X, Y projection plane (projection plane) 4 consisting of a plane, and then convert it to an η, ξ plane by eyeball conversion. Become.

First, in the method of constructing the three-dimensional image, coordinate conversion by central projection will be described. When projecting each tomographic image on the projection surface by the central projection, conversion of pixel coordinates of each tomographic image into coordinates on the projection surface is performed as follows.

In the example shown in FIG. 4, the coordinate system is set so that the projection plane, the tomographic image plane, and the xy plane are parallel to each other for simplification of description. In FIG. 4, x, y,
z is each axis of the three-dimensional coordinate system (x, y, z), and point e (x1,
y1, d1) is the position of the viewpoint e, point P (X, Y) is a point on the projection surface (corresponding to the display screen) 21, and point S (x0, y0,
d0) is a point where the straight line 22 passing through the point e (x1, y1, d1) and the point P (X, Y) intersects with the tomographic image 23A.

Further, D is the position of the projection surface 21 of the projection surface 21 (on the z-axis) and can be arbitrarily set.

D0 is the position of the tomographic image 23A (on the z-axis),
Determined at the time of measurement.

D1 is the z coordinate of the viewpoint e.

According to this, the following equation holds.

X = {(D-d1) / (d0-d1)} × (x0-x1) + x1 (1) Y = {(D-d1) / (d0-d1)} × (y0-y1) + Y1 (2) x0 = {(d0-D) / (d1-D)} * (x1-x) + X ... (3) y0 = {(d0-D) / (d1-D)} * (y1-- y) + Y (4) When a projected image is displayed on a display screen (not shown) corresponding to the projection surface 21 with 512 pixels in the vertical direction and 512 pixels in the horizontal direction, X and Y are from -256 to +256. Take a value. On the tomographic image 23A of d0 for each X and Y, x0 and y0 are determined by the above equations (3) and (4), and which point should be projected. Since there are a plurality of tomographic images 23 and a plurality of d0, a plurality of points x0 and y0 to be projected are determined for one set of X and Y.

In the same coordinate system, tomographic images 23B to 23E are prepared in addition to the tomographic image 23A, and a view seen from the y-axis direction is shown in FIG. 5 (a). In FIG. 5A, the tomographic images 23A to 23E are tomographic images obtained at equal intervals in the same direction on the same object (equal intervals in the illustrated example, but not necessarily equal intervals). In the tomographic image 23B, the organ regions B1, B2, B3 are emphasized and written. When the organ areas B1, B2, B3 are projected on the projection surface 21, B1 ',
B2 'and B3'. Similarly, when the organ regions C1 and C2 of the tomographic image 23C are projected on the projection surface 21, they become C1 'and C2'.

Here, the projection data (here, B1 ',
When writing B2 ', B3'; C1 ', C2') in the display memory (not shown), projection data existing farther from the viewpoint e is written first in order to produce a three-dimensional effect. ,
The projection data closer to it will be overwritten later. Therefore, here, the projection data B is calculated from the projection data C1 and C2.
Since 1, B2 and B3 exist farther than the viewpoint e, the projection data B1 ', B2' and B3 'are written first and the projection data C1' and C2 'are overwritten later. In FIG. 7A, projection data B1 ', B2', B3 '; C1
′ And C2 ′ are shown separately from the projection plane 21,
This is the projection data B1 ', B2', which is written in the display memory.
The projection data B1 ', B2', B3 'written first is only for making the order of B3'; C1 ', C2' easier to understand.
Also, the projection data C1 'and C2' that are overwritten are actually written on the projection surface 21.

FIG. 5B is a more generalized view than FIG. 5A and shows an example in which the projection plane and the tomographic image plane are not parallel. In this case, the tomographic images 23A, 23B, 23C
It is necessary to create the tomographic images 23a, 23b, 23c, ... Others are the same as in the case of FIG. In addition,
b1 ';c1', c2 ';d1' are organ regions b1; c1, c2; on the interpolated tomographic images 23b, 23c, 23d.
This is the projection data of d1.

FIG. 6 is a diagram for explaining the coordinate conversion by the central projection when the viewpoint, tomographic image and projection plane have a more complicated positional relationship, and is S point (x0, z0, on the tomographic image 23.
It shows that the projection result of (y0) becomes P point (x, y, z) on the projection plane.

In the projection of the tomographic image 23 on the projection plane 4 by the central projection in FIG. 6, the pixel coordinates of the tomographic image 23 are converted into the coordinates on the projection plane 4 as follows. Where a is the intersection of the x-axis and the projection plane 4, b
Is the intersection of the y axis and the projection plane 4, and c is the z axis and the projection plane 4.
Is the point of intersection.

Further, α is an angle formed by a line obtained by projecting a perpendicular line drawn from the origin onto the projection plane 4 on the zx plane with the x axis. Β is an angle e point (x1, y1, y1) formed by the perpendicular line with the xz plane. z1) is the viewpoint e
, Point P (x, y, z) is a point on the projection plane (corresponding to the display screen) 4, point S (x0, z0, y0) is point e (x1,
y1, z1) and the point where the straight line 22 passing through the point P (x, y, z) and the tomographic image 23 intersect, the following formula is established.

First, the projection plane 4 is expressed by (x / a) + (y / b) + (z / c) = 1 (5). A straight line 22 passing through the point e (x1, y1, z1) and the point P (x, y, z) is (x0-x) / (x1-x) = (y0-y) / (y1-y) = (Z0-z) / (z1-z) (6)

The projection plane 4 is at point C1 (xc1, yc1, zc
When passing through 1), k1 = sinα k2 = cosα / sinβ k3 = cosα · cosβ / sinβ ai = 1 / a bi = 1 / b ci = 1 / c, and z = [X · k1−Y · k2-yc1 * K3-{(ci * k3 * zc1) / bi} + {(ai * k3 * X) / (bi * cos [alpha])}-{(ai * k3 * xc1) / bi}] / [1-{(ci · K3) / bi} + {(ai · k3 · sinα) / (bi · cosα)}] (7) x = (X−z · sinα) / cosα (8) y = [yc1 + {-ci -(Z-zc1) -ai * (x-xc1)}] / bi (9) Here, the point C1 (xc1, yc1, zc1) is, for example, from the viewpoint e (x1, y1, z1). As a point where the perpendicular line drawn to the projection plane 4 and the projection plane 4 intersect (the distance between this point and the viewpoint e is h), zc1 = z1 +-[h / sqrt ^{{1+ (c 2 / a 2} ) + (c 2 / b 2)}] ( "z1 + -" in "-" when the z0 <zc1) ... (10) xc1 = x1 + {c · (z1-zc1) / A} (11) yc1 = y1 + {c · (z1−zc1) / b} (12) may be used.

When a projected image is displayed on a display screen (not shown) corresponding to the projection plane 4 with 512 pixels in the vertical direction and 512 pixels in the horizontal direction, X and Y take values from -256 to +256. Listed above for each X and Y (7),
X and y are determined by the equations (8) and (9). x1 at point e,
Since y1 and z1 are given arbitrarily, the following (13), (14)
From the equation, the coordinate x0 of the pixel S point on the tomographic image of y0 = d0,
z0 is determined.

X0 = {(d0-y) / (y1-y)} × (x1-x) + x (13) z0 = {(d0-y) / (y1-y)} × (z1-z) + Z (14) Since there are a plurality of tomographic images and a plurality of d0, a plurality of points x0 and y0 to be projected are determined for one set of X and Y.

Note that R in FIG. 6 indicates the distance from the viewpoint e to the point S, and this R is a parameter for obtaining the pixel value (luminance) at the point P. The pixel value at the point P is proportional to the value obtained by subtracting the above R from the maximum value Rmax of the set pixel value (luminance). This point P is (η,
Since it corresponds to the point (ξ), the pixel value is stored at the point (η, ξ).

The above coordinate conversion is performed for all points on the projection plane 4 corresponding to the display screen. In addition, all tomographic images 23 are performed. Furthermore, even if the three-dimensional image that is the resultant image is constructed,
It may be performed for each tomographic image.

FIG. 7 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied. In this FIG.
50 is a CPU, 51 is a main memory, 52 is a magnetic disk,
53 is a display memory and 55 is a mouse controller, which are connected to a common bus 57. Magnetic disk 52
Stores a plurality of tomographic images and a program for performing calculation of the method of the present invention.

The CPU 50 reads out these plural tomographic images and the program for execution calculation of the method of the present invention, performs calculation such as eyeball conversion using the main memory 51, sends the result to the display memory 53, and displays it on the CRT monitor. 54 is displayed. Mouse 56 connected to mouse controller 55
Specifies the viewpoint position and the like when performing calculations such as eyeball conversion.
The image that has undergone eyeball conversion and distortion correction is stored in the magnetic disk 52 as necessary.

[0048]

As described above, according to the present invention, the distortion of the projected image depending on the projection direction is corrected and the projection data (length or size) is prevented from being different due to the difference in the projection direction. The effect is that you can do it.

[Brief description of drawings]

FIG. 1 is a flow chart showing an outline of the method of the present invention.

FIG. 2 is a diagram illustrating the principle of distortion correction by eye conversion.

FIG. 3 is a diagram illustrating the principle of distortion correction by eyeball conversion.

FIG. 4 is a diagram for explaining conversion of tomographic image pixel coordinates into coordinates on a projection plane in a method of constructing a three-dimensional image.

FIG. 5 is a diagram for explaining conversion of pixel coordinates of a plurality of tomographic images into coordinates on the projection surface.

FIG. 6 is a diagram for explaining coordinate conversion by central projection when a viewpoint, a tomographic image, and a projection plane have a more complicated positional relationship.

FIG. 7 is a block diagram showing a hardware configuration example to which the method of the present invention can be applied.

FIG. 8 is an explanatory diagram of eyeball projection.

FIG. 9 is an explanatory diagram of a center projection method and distortion.

[Explanation of symbols]

3 Projection sphere 4 Projection plane X, Y, Z Each axis of 3D coordinate system O Origin of 3D coordinate system e View point h Distance between viewpoint e and projection plane 4 R Radius of projection sphere 3 P Point on projection plane 4 (X1, Y1) ψ Angle between straight line OP and X axis Q Point on projection spherical surface 3 corresponding to point P on projection plane 4 (intersection point of straight line Pe and projection spherical surface 3) θ Straight line Z1 Q and Z axis Formed angle L A line segment on a straight line OP having the same length as the arc OQ L'L on the projection spherical surface 3 η CRT display address (taken in parallel with X axis) ξ CRT display address (taken in parallel with Y axis) U Length of straight line eQ γ Angle between straight line segment eP and Z axis Length of straight line lowered perpendicular to Z axis from w Q

Claims (8)

[Claims] 1. A central projection method for projecting a projection target onto a projection surface by emitting light rays in a conical shape from a viewpoint, wherein the projection target is subjected to eyeball conversion after or after projection onto a projection surface consisting of a plane. A central projection method comprising re-projecting onto a projection plane composed of the plane. 2. The hemisphere conversion is two hemispheres obtained by dividing a spherical surface having a center on the line of sight into two in a direction perpendicular to the line of sight after or at the time of projection onto a plane projection surface. A re-projection to a projection surface composed of the plane through projection onto the projection surface (projection spherical surface) having a hemispherical surface far from the viewpoint as a projection surface. 1. The center projection method described in 1. 3. The central projection method according to claim 1, wherein the diameter of the spherical surface is equal to the distance from the viewpoint to the projection plane. 4. The center projection method according to claim 1, 2 or 3, wherein an image size of a projected image on the projection plane is larger than an image size of an image projected after being corrected by eyeball conversion. . 5. The central projection method according to claim 1, wherein the projection target is data input by an input device. 6. The center projection method according to claim 1, wherein the projection target is data obtained as a result of calculation by a calculation device. 7. The data obtained as a result of calculation by the calculation device is a tomographic image including a tomographic image obtained by decomposing a volume image obtained by three-dimensional measurement.
The central projection method described in. 8. The center projection method according to claim 6, wherein the data obtained as a result of calculation by the calculation device is a three-dimensional image formed by using a general center projection method.