A camera calibration method

Abstract

The present invention discloses a method for camera calibration. First, a calibration plate is selected, and a circular calibration plate with an inner and outer circle radius ratio of 1:2 is selected. Then the circular calibration plate is photographed. In order to better reflect the effect of the present invention, the angle between the calibration plate and the camera should be increased as much as possible during the shooting process, so as to better reflect the effect of eliminating eccentricity errors in the present invention. The center point extraction method used in the present method can effectively eliminate the perspective error caused by projection transformation, and is one of the key steps to improve the accuracy of camera calibration. By detecting and extracting the center point in the image, the feature points on the surface of the object can be obtained, and these feature points have stable positions at different angles and positions. When performing camera calibration, the stability of these feature points enables us to more accurately estimate the intrinsic and extrinsic parameters of the camera, thereby eliminating the perspective distortion caused by projection transformation.

Description

Technical Field

[0001] The present invention relates to the technical field of camera calibration, and in particular to a camera calibration method. Background Art

[0002] One of the basic tasks of computer vision is to calculate the geometric information of objects in three-dimensional space from the image information obtained by the camera, and to reconstruct and identify the objects. The relationship between the three-dimensional geometric position of a point on the surface of a spatial object and its corresponding point in the image is determined by the geometric model of camera imaging. These geometric model parameters are camera parameters. The process of obtaining these camera parameters is called camera calibration.

[0003] At present, the most mainstream method for camera calibration is Zhang Zhengyou calibration method, which uses a checkerboard calibration plate and uses the intersection of the checkerboard as the corner point of camera calibration. However, when the calibration image is blurred, there will be a big problem in extracting the corner point of the checkerboard calibration. The positioning accuracy will be greatly improved by using the center of the circle as the feature point. Therefore, in high-precision camera calibration, plane targets with the center of the circle as the mark point are widely used.

[0004] However, when the center of the circle is used as the feature point for calibration, the eccentricity error of the circle is inevitable, because the circle will become an ellipse after the projection transformation, and its center will become difficult to find due to the projection transformation. This will greatly reduce the accuracy of camera calibration using the center of the circle as the feature point. Summary of the invention

[0005] The purpose of the present invention is to provide a camera calibration method to solve the problems raised in the above background technology.

[0006] To achieve the above object, the present invention provides the following technical solution: a camera calibration method, specifically comprising the following steps:

[0007] Step 1: Select the calibration plate. The calibration plate uses a circular ring with 9 rows and 11 columns. The circular ring calibration plate with an inner and outer circle radius ratio of 1:2 is selected. According to the principle of projective geometry, the intersection ratio of collinear points is:

[0008]

[0009] According to the intersection ratio formula, find the intersection ratio of four of the five points where a straight line passing through the center of the circle intersects with the large and small circles, and use the intersection ratio of the four points including the center of the circle;

[0010] Step 2: Get the initial calibration plate image and preprocess the image to make it a picture that can be used for camera calibration;

[0011] Step 3: First find the center of each large ellipse in the image, and then find the center of each small ellipse in the image;

[0012] Step 4: For each ring, connect the centers of the two ellipses to get a straight line. Here we need to use a corollary:

[0013] Assume the standard equation of the ellipse is:

[0014] p T Ep=0 (1.2)

[0015] in:

[0016]

[0017] p = [xy 1] T (1.4)

[0018] When the equation is a perfect circle, the equation becomes:

[0019] p T Cp=0(1.5)

[0020]

[0021] During the camera calibration process, the conversion formula from the world coordinate system to the image coordinate system is:

[0022]

[0023] The projection matrix H can be expressed as:

[0024]

[0025] Assuming that the projection of the circle on the image is an ellipse, then combining formulas (1.2), (1.5) and (1.7) yields:

[0026] sE=H -T CH -1 (1.9)

[0027] Finally, the ellipse parameters are solved and the conclusion is drawn:

[0028] The centers of the two projected ellipses are in a straight line with the true projection center;

[0029] Therefore, according to this conclusion, the center of the true projection must be on this straight line;

[0030] Find the intersection points of the straight line and the large and small ellipses respectively. Since the radius ratio of the inner and outer circles on the calibration plate is fixed, find the coordinates of the four points where a straight line passing through the center of the circle intersects with the concentric circles, and then use formula (1.1) to find the intersection ratio based on the coordinates;

[0031] For projective transformation, the cross ratio is determined by the invariance, namely:

[0032] (p1,p2;p3,p4)=(p1',p2';p3',p4')(1.10)

[0033] p1′, p2′, p3′, p4′ are the corresponding points after projection of the four points;

[0034] Step 5: According to the cross ratio invariance after the projection transformation, the true projection center is calculated using the cross ratio invariance;

[0035] Step 6: For one of the intersection points of the straight line just fitted by the two circle centers and the inner circle, draw a tangent line of the small ellipse through this point, and the tangent line intersects the outer circle at two points;

[0036] Step 7: Connect these two points with the intersection of the straight line and the other side of the outer circle; these two lines must also be tangents of the small ellipse, and the three tangents form a triangle;

[0037] Step 8: Connect the tangent point of the two tangents to the opposite end points of the triangle formed by the three tangents. Similarly, use the cross ratio invariance to find the two projection centers again;

[0038] Step 9: Use the average value of the three projection centers to fit an accurate center as the landmark point for camera calibration.

[0039] In step 3, the center of the circle is first obtained by using a common center of circle extraction method. The center of the circle obtained here is inaccurate, but is approximate to the true center of the circle.

[0040] In step 4, each circular ring image is cut out by using the obtained circle center as the center and fixing the length and width, that is, the entire calibration plate image is divided into n small circular ring images, which is convenient for subsequent processing; ellipse fitting is performed on each circular ring image, and the parameters of the large ellipse and the small ellipse are respectively obtained.

[0041] In step 4, the center point of the true projection is assumed to be point c′. Using the principle of collinearity, the center c′ of the true projection is on the connecting line between the center c1′ of the large ellipse and the center c2′ of the small ellipse. The center c1′ of the large ellipse is connected to the center c2′ of the small ellipse, and the points p1′, p2′ and p3′, p4′ intersect with the large ellipse. Among them, p1′, p2′, p3′, p4′ are collinear with point c′. Because the elliptical ring is obtained by projection transformation of concentric rings with a radius of 1:2, according to the cross ratio invariance, the four points p1′, p2′, p3′, and c′ satisfy the cross ratio invariance.

[0042] In step 4, the parameters of the large ellipse and the small ellipse are known, then the coordinates of the centers of the large ellipse and the small ellipse and the standard equation of the ellipse are known, and a straight line is obtained according to the coordinates of the two points, and the straight line equation and the ellipse equation are combined to obtain the intersection points of the straight line with the large ellipse and the small ellipse, that is, the four points p1′, p2′, p3′, and p4′; the coordinates of c′ can be obtained by using the intersection ratio invariance; then a tangent line of the small ellipse is drawn through point p3′, intersecting the large ellipse at points p5′ and p6′, connecting p5′ and p2′; p6′ and p2′, since the radius of the concentric circles of the calibration plate is 1:2, these two straight lines must be tangent to the small circle, and after the projection transformation, the relationship between the ellipse and the straight line remains unchanged, so these two straight lines are also tangent to the ellipse.

[0043] In step 8, the tangent points p7′ and p8′ of the two tangents are respectively connected with the diagonal points p6′ and p5′ to obtain two straight lines. By using the invariance of the cross ratio, the coordinates of the two real projection centers are also calculated. By taking the average value of these three coordinates, the most accurate coordinate can be fitted.

[0044] Compared with the prior art, the present invention has the following beneficial effects:

[0045] The center point extraction method used in this method can effectively eliminate the perspective error caused by projection transformation, and is one of the key steps to improve the accuracy of camera calibration. By detecting and extracting the center point in the image, we can obtain the feature points on the surface of the object, which have stable positions at different angles and positions. When calibrating the camera, the stability of these feature points enables us to more accurately estimate the intrinsic and extrinsic parameters of the camera, thereby eliminating the perspective distortion caused by projection transformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is the overall flow chart of the present invention.

[0047] Figure 2 This is a schematic diagram of a ring before projection transformation.

[0048] Figure 3 Schematic diagram of the size ellipses formed by the ring after projection transformation. DETAILED DESCRIPTION

[0049] The following will be combined with the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0050] See also Figure 1-3The present invention provides a camera calibration method, which specifically includes the following steps:

[0051] Step 1: Select the calibration plate. The calibration plate uses a circular ring with 9 rows and 11 columns. The circular ring calibration plate with an inner and outer circle radius ratio of 1:2 is selected. According to the principle of projective geometry, the intersection ratio of collinear points is:

[0052]

[0053] According to the intersection ratio formula, find the intersection ratio of four of the five points where a straight line passing through the center of the circle intersects with the large and small circles, and use the intersection ratio of the four points including the center of the circle;

[0054] Step 2: Get the initial calibration plate image and preprocess the image to make it a picture that can be used for camera calibration;

[0055] Step 3: First find the center of each large ellipse in the image, and then find the center of each small ellipse in the image;

[0056] Step 4: For each ring, connect the centers of the two ellipses to get a straight line. Here we need to use a corollary:

[0057] Assume the standard equation of the ellipse is:

[0058] p T Ep=0 (1.2)

[0059] in:

[0060]

[0061] p = [xy 1] T (1.4)

[0062] When the equation is a perfect circle, the equation becomes:

[0063] p T Cp=0 (1.5)

[0064]

[0065] During the camera calibration process, the conversion formula from the world coordinate system to the image coordinate system is:

[0066]

[0067] The projection matrix H can be expressed as:

[0068]

[0069] Assuming that the projection of the circle on the image is an ellipse, then combining formulas (1.2), (1.5) and (1.7) yields:

[0070] sE=H -T CH -1 (1.9)

[0071] Finally, the ellipse parameters are solved and the conclusion is drawn:

[0072] The centers of the two projected ellipses are in a straight line with the true projection center;

[0073] Therefore, according to this conclusion, the center of the true projection must be on this straight line;

[0074] Find the intersection points of the straight line and the large and small ellipses respectively. Since the radius ratio of the inner and outer circles on the calibration plate is fixed, find the coordinates of the four points where a straight line passing through the center of the circle intersects with the concentric circles, and then use formula (1.1) to find the intersection ratio based on the coordinates;

[0075] Projective transformation, the cross ratio is invariant, that is:

[0076] (p1,p2;p3,p4)=(p1',p2';p3',p4')(1.10)

[0077] p1′, p2′, p3′, p4′ are the corresponding points after projection of the four points;

[0078] Step 5: According to the cross ratio invariance after the projection transformation, the true projection center is calculated using the cross ratio invariance;

[0079] Step 6: For one of the intersection points of the straight line just fitted by the two circle centers and the inner circle, draw a tangent line of the small ellipse through this point, and the tangent line intersects the outer circle at two points;

[0080] Step 7: Connect these two points with the intersection of the straight line and the other side of the outer circle; these two lines must also be tangents of the small ellipse, and the three tangents form a triangle;

[0081] Step 8: Connect the tangent point of the two tangents to the opposite end points of the triangle formed by the three tangents. Similarly, use the cross ratio invariance to find the two projection centers again;

[0082] Step 9: Use the average value of the three projection centers to fit an accurate center as the landmark point for camera calibration.

[0083] First, use the ordinary center of circle extraction method to obtain the center of the circle. The center of the circle obtained here is inaccurate, but it is close to the true center of the circle.

[0084] Using the obtained center of the circle as the center, fixing the length and width, each circular ring image is cut out, that is, the entire calibration plate image is divided into n small circular ring images, which is convenient for subsequent processing; ellipse fitting is performed on each circular ring image, and the parameters of the large ellipse and the small ellipse are obtained respectively.

[0085] Assume that the center point of the true projection is point c′. Using the principle of collinearity, the center c′ of the true projection is on the connecting line of the center c1′ of the large ellipse and the center c2′ of the small ellipse; connect the center c1′ of the large ellipse and the center c2′ of the small ellipse, intersect with the large ellipse at points p1′, p2′, and intersect with the small ellipse at points p3′, p4′; among them, p1′, p2′, p3′, p4′ are collinear with point c′; because the elliptical ring is obtained by projection transformation of concentric rings with a radius of 1:2; so according to the cross ratio invariance, the four points p1′, p2′, p3′, and c′ satisfy the cross ratio invariance.

[0086] The parameters of the large ellipse and the small ellipse are known, so the coordinates of the centers of the large ellipse and the small ellipse and the standard equation of the ellipse are known. The straight line is obtained according to the coordinates of the two points, and the equation of the straight line and the equation of the ellipse are combined to obtain the intersection points of the straight line with the large ellipse and the small ellipse, that is, the four points p1′, p2′, p3′, and p4′; the coordinates of c′ can be obtained by using the intersection ratio invariance; then a tangent line of the small ellipse is drawn through point p3′, intersecting the large ellipse at points p5′ and p6′, connecting p5′ and p2′; p6′ and p2′, since the radius of the concentric circles of the calibration plate is 1:2, these two straight lines must be tangent to the small circle, and after the projection transformation, the relationship between the ellipse and the straight line remains unchanged, so these two straight lines are also tangent to the ellipse.

[0087] The tangent points p7′ and p8′ of the two tangents are connected to the diagonal points p6′ and p5′ to obtain two straight lines. Using the invariance of the cross ratio, the coordinates of the two real projection centers are also obtained. The average value of these three coordinates can be used to fit the most accurate coordinate.

[0088] Although the present invention has been described in detail with reference to the aforementioned embodiments, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments, or to make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A camera calibration method, characterized in that: The specific steps include: Step 1: Select the calibration plate. The calibration plate uses a circular ring with 9 rows and 11 columns. The circular ring calibration plate with an inner and outer circle radius ratio of 1:2 is selected. According to the principle of projective geometry, the intersection ratio of collinear points is: According to the intersection ratio formula, find the intersection ratio of four of the five points where a straight line passing through the center of the circle intersects with the large and small circles, and use the intersection ratio of the four points including the center of the circle; Step 2: Obtain the initial calibration plate image and preprocess the image to make it a picture for camera calibration; Step 3: First find the center of each large ellipse in the image, and then find the center of each small ellipse in the image; Step 4: For each ring, connect the centers of the two ellipses to get a straight line. Here we need to use a corollary: Assume the standard equation of the ellipse is: p T Ep=0(1.2) in: p=[x y 1] T (1.4) When the equation is a perfect circle, the equation becomes: p T Cp=0(1.5) During the camera calibration process, the conversion formula from the world coordinate system to the image coordinate system is: The projection matrix H is expressed as: Assuming that the projection of the circle on the image is an ellipse, then combining formulas (1.2), (1.5) and (1.7) yields: se=H -T CH -1 (1.9) Finally, the ellipse parameters are solved and the conclusion is drawn: The centers of the two projected ellipses are in a straight line with the true projection center; Therefore, according to this conclusion, the center of the true projection must be on this straight line; Find the intersection points of the straight line and the large and small ellipses respectively. Since the radius ratio of the inner and outer circles on the calibration plate is fixed, find the coordinates of the four points where a straight line passing through the center of the circle intersects with the concentric circles, and then use formula (1.1) to find the intersection ratio based on the coordinates; Projective transformation, the cross ratio is invariant by: (p1,p2;p3,p4)=(p1',p2';p3',p4')(1.10) p1′, p2′, p3′, p4′ are the corresponding points after projection of the four points; Step 5: According to the cross ratio invariance after the projection transformation, the true projection center is calculated using the cross ratio invariance; Step 6: For one of the intersection points of the straight line just fitted by the two circle centers and the inner circle, draw a tangent line of the small ellipse through this point, and the tangent line intersects the outer circle at two points; Step 7: Connect these two points with the intersection of the straight line and the other side of the outer circle; these two lines must also be tangents of the small ellipse, and the three tangents form a triangle; Step 8: Connect the tangent point of the two tangents to the opposite end points of the triangle formed by the three tangents. Similarly, use the cross ratio invariance to find the two projection centers again; Step 9: Use the average value of the three projection centers to fit an accurate center as the landmark point for camera calibration.

2. A camera calibration method according to claim 1, characterized in that: In step 3, the center of the circle is first obtained by using a common center of circle extraction method. The center of the circle obtained here is inaccurate, but is approximate to the true center of the circle.

3. The camera calibration method according to claim 1, characterized in that: In step 4, each circular ring image is cut out with the obtained circle center as the center and the length and width fixed, and the entire calibration plate image is divided into n small circular ring images, which is convenient for subsequent processing; ellipse fitting is performed on each circular ring image, and the parameters of the large ellipse and the small ellipse are respectively obtained.

4. The camera calibration method according to claim 1, characterized in that: In step 4, the center point of the true projection is assumed to be point c′. Using the principle of collinearity, the center c′ of the true projection is on the connecting line between the center c1′ of the large ellipse and the center c2′ of the small ellipse. The center c1′ of the large ellipse is connected to the center c2′ of the small ellipse, and the points p1′, p2′ and p3′, p4′ intersect with the large ellipse. Among them, p1′, p2′, p3′, p4′ are collinear with point c′. Because the elliptical ring is obtained by projection transformation of concentric rings with a radius of 1:2, according to the cross ratio invariance, the four points p1′, p2′, p3′, and c′ satisfy the cross ratio invariance.

5. The camera calibration method according to claim 1, characterized in that: In step 4, the parameters of the large ellipse and the small ellipse are known, so the coordinates of the centers of the large ellipse and the small ellipse and the standard equation of the ellipse are known, and a straight line is obtained according to the coordinates of the two points. The straight line equation and the ellipse equation are combined to obtain the intersection points of the straight line with the large ellipse and the small ellipse, namely, points p1′, p2′, p3′, and p4′; the coordinates of c′ can be obtained by using the intersection ratio invariance; then a tangent line of the small ellipse is drawn through point p3′, intersecting the large ellipse at points p5′ and p6′, connecting p5′ and p2′; p6′ and p2′, since the radius of the concentric circles of the calibration plate is 1:2, these two straight lines must be tangent to the small circle, and after the projection transformation, the relationship between the ellipse and the straight line remains unchanged, so these two straight lines are also tangent to the ellipse.

6. The camera calibration method according to claim 1, characterized in that: In step 8, the tangent points p7′ and p8′ of the two tangents are respectively connected with the diagonal points p6′ and p5′ to obtain two straight lines. By using the invariance of the cross ratio, the coordinates of the two real projection centers are also calculated. The average value of these three coordinates is calculated to fit the most accurate coordinate.

Images