WO2015133526A1

WO2015133526A1 - Image analysis method, image analysis device, and image analysis program

Info

Publication number: WO2015133526A1
Application number: PCT/JP2015/056374
Authority: WO
Inventors: 謙陳; 海元呉
Original assignee: 国立大学法人和歌山大学
Priority date: 2014-03-07
Filing date: 2015-03-04
Publication date: 2015-09-11
Also published as: JP2015170181A

Abstract

Provided is an image analysis method that is able to determine the position corresponding to the center of a circle in an image capturing the circle. The image analysis method, which determines a point (c0) corresponding to the center of a circle (C, D) in an image capturing the circle (C, D) on a plane, contains a processing step for determining the position of a first corresponding point (c0) on the image on the basis of the relationship between the compound ratio of a first point (C0, D0), which is the center of the circle (C, D), a second point (E, F) and third point (E', F') at which a center line passing through the first point (C0, D0) intersects the circle (C, D), and a fourth point (A) at which the center line and a line (H) at infinity intersect, and the compound radio of first through fourth corresponding points (c0, e, f, e', f') on the image and corresponding to the first through fourth points.

Description

Image analysis method, image analysis apparatus, and image analysis program

The present invention relates to an image analysis method, an image analysis apparatus, and an image analysis program for obtaining a position corresponding to the center of a circle in an image obtained by photographing the circle.

When an image taken by a camera is processed to measure the position of an object, the camera needs to be calibrated. As a calibration method, a position and orientation, which are one of external parameters of the camera, are obtained from a marker image of a specific pattern.
As the marker, those having various shapes such as a rectangular shape, a circular shape, or a lattice shape are used. In particular, since the circular marker has a simple shape, it has an advantage that it can be easily and precisely created (see, for example, Patent Document 1).

JP-A-8-171627

When camera calibration is performed using a circular marker, information on coordinates on the image corresponding to the center of the marker is required. Conventionally, the marker has been devised so that the center of the marker is known or the position of the center can be specified to some extent. For example, in the technique described in Patent Document 1, a density gradient is provided from the outer periphery to the center of a circular marker, and coordinates on the image corresponding to the center of the circle are obtained by using this density gradient.
Therefore, conventionally, it has been difficult to use a circle whose center position is completely unknown as a marker. However, if such use becomes possible, for example, any circle existing within the shooting range of the camera can be used as a marker, so that the range of utilization is greatly expanded, which is very beneficial.

An object of the present invention is to provide an image analysis method, an image analysis apparatus, and an image analysis program that can obtain a position corresponding to the center of a circle in an image obtained by photographing the circle.

The present invention is an image analysis method for obtaining a point corresponding to the center of a circle in an image obtained by photographing a circle on a plane,
The first point which is the center of the circle, the second point and the third point where the center line passing through the first point and the circle intersect, and the center line and the infinity line intersect. Based on the relationship between the cross ratio for the fourth point and the cross ratio for the first to fourth corresponding points on the image corresponding to the first to fourth points, It is characterized in that the position of one corresponding point is obtained.

In the analysis method as described above, the cross ratio at the first to fourth points related to the circle provided on the plane and the cross ratio at the first to fourth corresponding points on the projected image are invariant. (Same) relationship. On the other hand, the length between the first point and the second point is the same as the length between the first point and the third point, and the fourth point is the infinity point, so that The cross ratio at the first to fourth points is a predetermined value (see formula (3) described later). Therefore, in the analysis method of the present invention, it is possible to obtain a relational expression that substantially uses only the first to fourth corresponding points, the coordinates of the second to fourth corresponding points acquired from the image, and the relationship. The first corresponding point that is an image of the center (first point) of the circle can be easily obtained by the equation.

In the present invention described above, the following method can be adopted to set the fourth corresponding point. That is, a first intersection of a pair of straight lines on an image corresponding to a pair of straight lines parallel to each other set in two circles on the same plane or two parallel planes, and two circles. A second intersection of another pair of straight lines on the image corresponding to another pair of straight lines parallel to each other is obtained, and a straight line passing through the first and second intersections is defined as an image of the infinite line. The intersection of the far-line image and the straight line passing through the second and third corresponding points on the image can be set as the fourth corresponding point.

The pair of parallel straight lines may include a straight line passing through the intersections of two symmetrical tangents common to the two circles and the respective circles.
Further, the pair of straight lines parallel to each other is a straight line that passes through the intersection of one tangent common to the two circles and each circle, and the intersection between the center line passing through the centers of the two circles and each circle. May be included.

The present invention is an image analysis device for obtaining a point corresponding to the center of the circle in an image obtained by photographing a circle on a plane,
The first point which is the center of the circle, the second point and the third point where the center line passing through the first point and the circle intersect, and the center line and the infinity line intersect. Based on the relationship between the cross ratio for the fourth point and the cross ratio for the first to fourth corresponding points on the image corresponding to the first to fourth points, An image analysis apparatus comprising an analysis unit for obtaining a position of one corresponding point.

Further, the present invention is an image analysis program for obtaining a point corresponding to the center of the circle in an image obtained by photographing a circle on a plane,
The first point which is the center of the circle, the second point and the third point where the center line passing through the first point and the circle intersect, and the center line and the infinity line intersect. Based on the relationship between the cross ratio for the fourth point and the cross ratio for the first to fourth corresponding points on the image corresponding to the first to fourth points, The computer is made to function as an analysis unit for obtaining the position of one corresponding point.

According to the present invention, it is possible to obtain the position corresponding to the center of the circle in the image of the circle.

(A) is a schematic block diagram of the image-analysis apparatus based on one Embodiment of this invention, (b) is a top view of the circle set on the plane. It is plane explanatory drawing which shows the relationship of two circles on a plane. It is plane explanatory drawing which shows the relationship of the two ellipses on an image. It is a flowchart which shows the process sequence of an image analyzer.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1A is a schematic configuration diagram of an image analysis apparatus according to an embodiment of the present invention, and FIG. 1B is a plan view of a circle set on a plane.
The image analysis device 10 includes a camera 11 that captures an imaging target, and a processing device 12 that performs analysis processing on an image (video) of the camera 11.
Then, the image analysis apparatus 10 of the present embodiment captures two circles C and D set on one plane by the camera 11 and analyzes the images by the processing apparatus 12 to analyze the center C0 of the circles C and D. , D0, the point (coordinates) on the image is obtained.

In the example shown in FIG. 1, any two circles C and D (see FIG. 1B) are set on the plane P. The circles C and D may be drawn directly on a plane, or may be an annular object placed on the plane. The center positions C0 and D0 of both circles C and D are unknown. And the camera 11 images the area | region containing two circles C and D from diagonally upward, for example. The two circles C and D picked up by the camera 11 are projected onto a plane Q perpendicular to the focus direction of the camera 11 and thus become elliptical images.

The image analysis apparatus 10 of the present embodiment captures the circles C and D whose center positions are unknown by the camera 11 and points (centers) corresponding to the centers C0 and D0 of the circles C and D in the ellipse in the image. The corresponding point) is obtained by the processing device 12. Then, the obtained center corresponding point can be used for calibration of the camera 11, for example.

The processing device 12 is configured by, for example, a personal computer, and includes a calculation unit such as a CPU, a storage unit such as a RAM, ROM, and HDD, an output unit such as a liquid crystal panel, an input unit such as a keyboard and a mouse, and various interfaces. ing. Then, when the arithmetic unit executes the program installed in the storage unit, an image captured by the camera 11 is captured, the image is analyzed, the analysis result is output, and the like. In particular, the processing device 12 functions as an analysis unit that obtains points on the image corresponding to the centers C0 and D0 of the circles C and D.

Hereinafter, the analysis procedure by the processing device 12 will be described in detail.
First, the analysis method of the present embodiment uses the fact that the “cross ratio” is invariant between a circle on a plane and an ellipse that is an image of the circle. The cross ratio refers to the ratio of the lengths of directed line segments composed of four points on the same straight line in projective geometry. For example, in FIG. 1, the cross ratio of four points a, b, c, d on a straight line passing through the centers C0, D0 of two circles C, D on the plane and the two ellipses on the corresponding image The cross ratio of the four points a ′, b ′, c ′, and d ′ is unchanged, and the following expression (1) is satisfied.

The left side of Equation (1) indicates the cross ratio at the points a, b, c, and d of the circles C and D on the plane, and the right side is the points a ′, b ′, and c ′ of the ellipses c and d on the image. , D ′.

Based on the above, the actual analysis method will be described specifically.
FIG. 2 is an explanatory plan view showing the relationship between two circles on the plane. FIG. 3 is an explanatory plan view showing the relationship between two ellipses on an image.
In FIG. 2, it is assumed that two tangent lines (common outer tangent lines) S1 and S2 are provided in two circles C and D. In this case, a straight line (C1C2) that connects the contact points C1 and C2 of the two tangent lines S1 and S2 and the circle C and a straight line (D1D2) that connects the contact points D1 and D2 of the tangent lines S1 and S2 and the circle D are parallel to each other. It becomes.

The straight line C1C2 and the straight line D1D2 are parallel. However, in projective geometry, both straight lines C1C2 and D1D2 are considered to intersect at an infinite point B. In FIG. 2, the locus reaching the infinity point B is indicated by a curved dotted line due to space limitations, but it is actually a straight line.

On the other hand, when two tangents s1 and s2 are provided in two ellipses c and d in FIG. The straight lines (c1c2) connecting the contact points d1 and d2 between the tangent lines s1 and s2 and the ellipse d are images of the straight lines C1C2 and D1D2 in FIG. 2, respectively. The straight line c1c2 and the straight line d1d2 have an intersection point b. Therefore, this intersection point b corresponds to the infinity point B in FIG. In FIG. 3 as well, the locus reaching the intersection of the straight line c1c2 and the straight line d1d2 is indicated by a curved dotted line due to space limitations, but in reality it is a straight line.

Here, the “cross ratio” relationship shown in Equation (1) is used. That is, in the circle C of FIG. 2, the four points B, C1, and C1 on the straight line (hereinafter referred to as “straight line C1C2”) passing through the point C1 and the point C2 are taken between the point C1 and the point C2. Consider the cross ratio of Cm and C2.

On the other hand, in FIG. 3, there are four points b, c1, cm, on a straight line (hereinafter referred to as “straight line c1c2”) that takes a midpoint cm between the points c1 and c2 and passes through the points c1 and c2. Consider the cross ratio of c2. Since both cross ratios are unchanged, the following equation (2) is satisfied.

On the left side of Equation (2), since point B is an infinite point, the lengths of line segment BC1 and line segment BC2 are each infinite ∞. On the other hand, since the point Cm is the midpoint between the points C1 and C2, the lengths of the line segment CmC1 and the line segment CmC2 have the same dimension. Therefore, the left side of the above equation (2) can be transformed as the following equation (3).

That is, the cross ratio of the four points B, C1, Cm, and C2 in FIG.
On the other hand, the cross ratio of the four points b, c1, cm, and c2 in FIG. 3 shown on the right side of the equation (2) can be modified as the following equation (4).

Therefore, the above equation (2) can be rewritten as the following equation (5) from the equations (3) and (4).

And the following formula (6) can be obtained by transforming the formula (5).

In Expression (6), the positions of the points b, c1, and c2 can be obtained from the coordinates on the image. Therefore, the position of the midpoint cm is calculated from the coordinates of these points b, c1, and c2 ( 6).

Similarly, the circle D in FIG. 2 and the ellipse d in FIG. 3 have the same relationship as the above equations (2) to (6). Therefore, similarly to the equation (6), the relationship of the following equation (7) can be obtained.

In the equation (7), the positions of the points b, d1, and d2 can be obtained from the coordinates on the image, so that the position of the midpoint dm is also calculated from the coordinates of the points b, d1, and d2 ( 7) can be obtained by calculation. The midpoints cm and dm are merely midpoints of the line segment c1c2 and the line segment d1d2 and are not points corresponding to the centers of the circles C and D.

Next, consider a straight line C2E and a straight line D2F in circles C and D on the plane in FIG. Points E and F are points where straight lines CmDm passing through the points Cm and Dm intersect with the circles C and D, respectively. Since the triangle CmC2E and the triangle DmD2F have a similar relationship, the straight line C2E and the straight line D2F are parallel to each other. However, in terms of projective geometry, the straight line C2E and the straight line D2F intersect at an infinite point (disappearance point) G.

The straight line H passing through the infinity point B where the straight line C1C2 and the straight line D1D2 intersect and the infinity point G where the straight line C2E and the straight line D2F intersect is an infinity line where all the infinite points on the plane are located. Therefore, the infinity point of the straight line CmDm is a point A that intersects the infinity line H. The straight line CmDm is a straight line that also passes through the centers of the circles C and D.

On the other hand, in FIG. 3, a straight line c2e and a straight line d2f in the ellipses c and d on the image are images of the straight line C2E and the straight line D2F in FIG. The straight line c2e and the straight line d2f have an intersection point g. This intersection point g corresponds to the infinity point G in FIG. Therefore, a straight line h passing through a point b where the straight line c1c2 and the straight line d1d2 intersect and a point g where the straight line c2e and the straight line d2f intersect is an image of the infinite line H in FIG.
A point a where a straight line cmdm passing through the point cm and the point dm intersects the straight line h is an image of the point A at infinity of the straight line CmDm in FIG.

Then, points E (second point) and point E ′ (third point) where the straight line CmDm in FIG. 2 intersects the circle C, an infinite point (fourth point) A, and the center of the circle C (first point) The four points with the point 1) C0 are the point e (second corresponding point) and the point e ′ (third corresponding point) where the straight line cmdm in FIG. 4) and the center of the ellipse c (the point corresponding to the center of the circle C; the first corresponding point) c0 correspond to each other, so that the respective cross ratios are invariable. . Therefore, the relationship of the following equation (8) can be obtained similarly to the above equation (6).

In the equation (8), the position of each point a, e, e ′ can be obtained from the coordinates on the image. Therefore, the position of the center c0 can be calculated from the coordinates of these points a, e, e ′. (8) can be obtained by calculation.

The same can be said for the circle D and the ellipse d. That is, the points F (second point) and F ′ (third point) where the straight line CmDm in FIG. 2 intersects the circle D, the infinity point (fourth point) A, and the center of the circle D (first point) The first four points D0 are the points f (second corresponding point) and the point f ′ (third corresponding point) where the straight line cmdm in FIG. 4) and the center of the ellipse d (the point corresponding to the center D0 of the circle D; the fourth corresponding point) d0 correspond to each other, so that the respective cross ratios are invariant. Become. Therefore, the relationship of the following equation (9) can be obtained similarly to the above equation (6).

In Expression (9), the position of each point a, f, f ′ can be obtained from the coordinates on the image, and therefore the position of the center d0 can be calculated from the coordinates of each point a, f, f ′. (9) can be obtained by calculation.

By the above procedure, the centers c0 and d0 of the ellipses c and d on the image obtained by projecting the centers C0 and D0 of the circles C and D on the plane can be obtained.

FIG. 4 is a flowchart showing a specific processing procedure of the image analysis apparatus 10 using the above analysis method.
First, in step S1, an image including circles C and D set on a plane is captured by the camera.
In step S2, information on the captured image is input to the processing device 12 and stored in the storage unit.

In step S3, the image information is read from the storage unit, the contours of the ellipses c and d are extracted from the image, and the equation of the curve is obtained by the calculation unit by fitting the curve to the contour. .
Next, in step S4, a straight line cmdm (see FIG. 3) passing through the centers of the ellipses c and d on the image is obtained by the calculation unit. Specifically, as described above, the intersection points b and g between the pair of straight lines c1c2 and d1d2 and the pair of straight lines c2e and d2f set using the common outer tangent of the ellipses c and d on the image. Is required. Then, the midpoint cm is determined from the contact points c1 and c2 of the common outer tangent line and the intersection point b using the above formula (6), and the above formula (7) is used from the contact points d1 and d2 of the common outer tangent line and the intersection point g. Thus, a midpoint dm is obtained, and a straight line cmdm passing through these midpoints cm and dm is obtained. Further, points e, e ′, f, and f ′ at which the straight line cmdm and the ellipses c and d intersect are obtained. Information such as the coordinates of each point c1, c2, d1, d2, cm, dm, e, e ', f, f' and the straight line cmdm is stored in the storage unit and read out for calculation as appropriate.

In step S5, a straight line h (see FIG. 3) corresponding to the infinity line H where all the infinity points on the plane on which the circles C and D are set is obtained by the calculation unit. Specifically, as described above, a straight line h passing through the intersection b of the pair of straight lines c1c2 and d1d2 and the intersection g of the pair of straight lines c2e and d2f is obtained. Information about the straight line h is stored in the storage unit and read out for calculation as appropriate.

In step S6, the centers c0 and d0 of the ellipses c and d are obtained by the arithmetic unit using the straight line cmdm and the straight line h. Specifically, first, an intersection point a between the straight line cmdm and the straight line h acquired in steps S3 and S4 is obtained. Then, from the coordinates of the intersection point a and the coordinates of the intersection points e and e ′ between the straight line cmdm and the ellipse c, the coordinate of the center c0 is obtained by the equation (8). From the coordinates of the intersections f and f ′, the coordinate of the center d0 is obtained by equation (9).

From the above procedure, the computing unit of the present embodiment is the first computing means for obtaining the equations of the ellipses c and d from the image, the second computing means for obtaining the straight line h, and the first computing means for obtaining the straight line cmdm. 3 and 4th operation means for obtaining the centers c0 and d0.
Information such as the obtained intersection point a and coordinates of the centers c0 and d0 is stored in the storage unit and is appropriately output via the output unit.

According to the embodiment described above, the cross ratio at four points including the infinity point A on the straight line CmDm passing through the centers C0 and D0 of the circles C and D is “1”. By calculating the cross ratio of the four points a, e, c0, e ′ (a, f, d0, f ′) on the corresponding image (equations (8), (9)), the centers c0, d0 can be easily obtained.
Therefore, even if the center position is an unknown circle, it can be used as a marker for camera calibration. For this reason, for example, any circle included in the imaging range of the camera, for example, a signboard, a sign, a monument, etc. arranged in the city is used as a marker, or a naturally occurring circle such as a ripple on the water surface is used. It becomes possible to do. In addition, it is possible to use a human black eye as a marker. In this case, the gaze direction can be estimated without depending on the posture of the head. Therefore, when such a usage method is applied to a head mounted display (HMD), an image displayed on the HMD can be changed according to the direction of the line of sight.

Moreover, since camera calibration is possible using a circle whose center position is unknown as a marker, for example, a panoramic image is generated from a multi-viewpoint image (video) using a plurality of cameras, or three-dimensional information is restored. Thus, a free viewpoint image can be generated.

The present invention is not limited to the above-described embodiment, and can be appropriately changed within the scope of the invention described in the claims.
For example, the two circles are not limited to being set on the same plane, and may be set on two planes parallel to each other, for example, two planes having different heights.
The two circles may have the same diameter. Further, the two circles may partially overlap if they are not completely inclusive.
Moreover, a part of the circle on the plane may disappear. In this case, prior to obtaining the point corresponding to the center of the circle (first corresponding point), the equation may be obtained from a partial ellipse that is an image of a circle shown on the image.

In the above embodiment, the common outer tangent lines S1, S2, s1, and s2 are provided in two circles or two ellipses, but a common inscribed line may be provided instead of or in addition to this. When both the common circumscribed line and the common inscribed line are provided, the image of the straight line passing through the centers C0 and D0 of the two circles C and D should be a straight line passing through the intersection of the common circumscribed line and the intersected point of the common inscribed line. Can do.

10: Image analysis device 11: Camera 12: Processing device (analysis unit)

Claims

In an image obtained by photographing a circle on a plane, an image analysis method for obtaining a point corresponding to the center of the circle,
The first point which is the center of the circle, the second point and the third point where the center line passing through the first point and the circle intersect, and the center line and the infinity line intersect. Based on the relationship between the cross ratio for the fourth point and the cross ratio for the first to fourth corresponding points on the image corresponding to the first to fourth points, An image analysis method characterized by obtaining a position of one corresponding point.
A first intersection of a pair of straight lines on an image corresponding to a pair of parallel lines set in two circles on the same plane or two parallel planes, and parallel to each other set in two circles A second intersection of the other pair of straight lines on the image corresponding to the other pair of straight lines, and a straight line passing through the first and second intersections as an image of the infinity line. 2. The image analysis method according to claim 1, wherein an intersection of the image and a straight line passing through the second and third corresponding points on the image is set as the fourth corresponding point.
3. The image analysis method according to claim 2, wherein the pair of straight lines parallel to each other includes a straight line passing through the intersections of two symmetrical tangents common to the two circles and each circle.
The pair of straight lines parallel to each other includes a straight line passing through the intersection of one tangent common to the two circles and each circle, and the intersection between the center line passing through the centers of the two circles and each circle, The image analysis method according to claim 2 or 3.
In an image obtained by photographing a circle on a plane, an image analysis device for obtaining a point corresponding to the center of the circle,
The first point which is the center of the circle, the second point and the third point where the center line passing through the first point and the circle intersect, and the center line and the infinity line intersect. Based on the relationship between the cross ratio for the fourth point and the cross ratio for the first to fourth corresponding points on the image corresponding to the first to fourth points, An image analysis apparatus comprising an analysis unit for obtaining a position of one corresponding point.
In an image obtained by photographing a circle on a plane, an image analysis program for obtaining a point corresponding to the center of the circle,
The first point which is the center of the circle, the second point and the third point where the center line passing through the first point and the circle intersect, and the center line and the infinity line intersect. Based on the relationship between the cross ratio for the fourth point and the cross ratio for the first to fourth corresponding points on the image corresponding to the first to fourth points, An image analysis program for causing a computer to function as an analysis unit for obtaining the position of one corresponding point.