CN104123725B - A kind of computational methods of single line array camera homography matrix H - Google Patents

Abstract

A method for calculating the homography matrix H of a single line array camera, the method uses the principle of cross-ratio invariance, and the 4-line calibration plate provided by the present invention, the 4 lines meet the following rules: , , , , combined with the imaging characteristics of the line-scan camera, the (x, y, z) coordinates on the D4 line can be calculated by using the cross-ratio invariance of the 4 collinear points on the image plane, and then the homography matrix H can be calculated.

Description

A Calculation Method of Homography Matrix H for Single Line Array Camera

technical field

The invention belongs to the field of camera calibration and relates to a calculation method of a homography matrix H from a target point to an imaging point of a single line array camera.

Background technique

Camera calibration is to determine the relationship between the three-dimensional geometric position of a point on the surface of a space object and its corresponding point in the image. Based on the established geometric model of camera imaging, the parameter model of the camera is solved from the image coordinates and world coordinates of known feature points. Camera calibration is a very critical link, the accuracy of the calibration results and the stability of the algorithm will directly affect the accuracy of the camera work results. Therefore, improving the camera calibration accuracy is the focus of camera calibration.

An important step is the homography matrix H from the target point to the imaging point. To obtain the homography matrix H, it is necessary to know the coordinates of the target point and the imaging point. The method used uses a calibration plate to obtain the coordinates of these two points. At present, the common punctuation boards include checkerboard marking boards, circular marking boards and equidistant stripe marking boards. The checkerboard calibration board can easily obtain the coordinates of the target point. To obtain the accurate coordinates of the imaging point, a relatively uniform motion between the single line array camera and the calibration board is required, which increases the complexity of the system. Using a circular calibration plate, if the speed of the relative uniform motion between the single-line array camera and the calibration plate is not set properly, the circle of the imaging plane obtained will be deformed, and the center of the circle cannot be effectively calculated, and thus the exact coordinates of the imaging point cannot be obtained. The equidistant fringe calibration plate can quickly obtain the x-axis or y-axis value of the target point and imaging point, but cannot obtain the value of the other coordinate axis.

To sum up, there are still some shortcomings in the current calculation method of the homography matrix H from the target point to the imaging point of the single-line array camera: the relatively uniform motion between the single-line array camera and the calibration plate makes it difficult to set the speed. The relative non-uniform motion between the camera and the calibration board makes it impossible to calculate the homography matrix H.

Contents of the invention

The purpose of the present invention is to provide a method for calculating the homography matrix H of a single-line array camera, so as to achieve relative non-uniform motion between the camera and the calibration plate, and to calculate the homography matrix H of the single-line array camera.

In order to achieve the above object, the method for calculating the homography matrix H of a single-line array camera of the present invention adopts a special 4-line calibration plate, utilizes the imaging characteristics of a single-line array camera and the cross-ratio invariance of collinear 4 points, and calculates the single-line Array camera homography matrix H. The steps of this method are as follows:

(1) Use the Hough algorithm to extract the lines in the image of the single-line array camera, take any line in the image plane, intersect this line with the 4 lines in the image of the 4-line calibration plate captured, and take the intersection points as a, b, c and d;

(2) Calculate the cross-ratio of imaging points a, b, c and d .

(3) Using cross-ratio invariance to obtain the cross-ratio of imaging points a, b, c and d corresponding to target points A, B, C and D , and then calculate the (x, y, z) coordinates of point D.

(4) Substituting point D and the corresponding imaging point coordinates of point D into the homography matrix H formula from the target point to the imaging point, the corresponding H matrix can be calculated.

The 4-line calibration board in the step (1), the 4 lines meet the following rules: , , , , It can be set according to the requirement.

The cross ratio of the four points a, b, c and d on the straight line in the step (2) is , ac is the distance between two points a and c. The same applies to bc, ad, and bd.

The cross ratio invariance in the step (3) is

The steps for calculating the (x, y, z) coordinates of point D in the step (3) are as follows:

(1), consider a virtual line D5, which is parallel and coplanar with D1, D2, D3, D1, D2, D3 and the intersection points of these four parallel lines with the y-axis through D point D5 are A', B', C' and D'. With cross-ratio invariance, we have

therefore,

(2) A, B, C and D are on the four calibration lines of the calibration board, so it can be obtained

Further available:

Since the 4 calibration lines of the calibration plate are coplanar, the z coordinate of the space coordinates of the target plate is , which can be set according to the needs, and the (x, y, z) coordinates of point D can be obtained.

The steps for calculating the homography matrix H in the step (4) are as follows:

(1) By the homography formula of ordinary line scan camera

Deriving the homography formula of linear single-array camera

is the scale parameter;

So the homography matrix H is

(2) According to the homography formula of the ordinary line array camera, according to the target point D (x, y, z) and the corresponding imaging point coordinate d (u), the zero coordinate point of the imaging coordinate is the vertex in the da direction, and it can be calculated The homography matrix H. The beneficial effects of the present invention are: the calculation method of the homography matrix H of the single-line array camera of the present invention adopts a special 4-line calibration plate, and utilizes the imaging characteristics of the single-line array camera and the cross-ratio invariance of the collinear 4 points to calculate the single-line The array camera homography matrix H solves the problem that the homography matrix H cannot be calculated due to non-uniform motion between the single line array camera and the calibration plate. The method is simple in system and less restrictive, and has great significance and practical value for the application of single line array camera calibration.

Description of drawings

Fig. 1 is a schematic flow chart of the method of the present invention;

Figure 2 is a schematic diagram of imaging with a single line array camera;

In Figure 2, F is the focal point of the line scan camera. a, b, c, and d are image points, and A, B, C, and D are target points corresponding to image points a, b, c, and d. A', B', C' and D' are the values of A, B, C and D on the y-axis. D1, D2, D3, and D4 are 4 coplanar calibration lines, and the virtual line D5 passes through point D and is parallel and coplanar with D1, D2, and D3.

detailed description

In order to better understand the technical solutions of the present invention, the implementation manners of the present invention will be described in detail below in conjunction with the accompanying drawings.

As shown in Fig. 1, the present invention first performs Hough operation on the obtained image to obtain the straight line in the image, and selects the target point to calculate the cross ratio. According to the characteristics of the single line array camera imaging system, the cross-ratio of the target point is obtained by combining the invariance of the cross-ratio. Use the equation of the calibration line in the calibration plate to obtain the coordinates of point D.

The concrete implementation of the present invention is as follows:

1. Use the Hough algorithm to extract the lines in the image captured by the single-line array camera, take a line in the image plane, and intersect this line with the captured 4-line calibration board (the 4 lines meet the following rules: , , , , It is the 4 lines in the image that can be set according to the requirements, and the intersection points are a, b, c and d;

2. Using the cross-ratio of imaging points a, b, c and d

, ac is the distance between two points a and c. The same applies to bc, ad, and bd.

3. Using cross-ratio invariance to obtain the cross-ratio of imaging points a, b, c and d corresponding to target points A, B, C and D , and then calculate the (x, y, z) coordinates of point D.

Step 1: Using cross-ratio invariance to get

Step 2: As shown in Figure 2, consider a virtual line D5, which is parallel and coplanar with D1, D2, D3, D1, D2, D3 and passing through D point D5, these four parallel lines intersect with the y-axis as A', B ', C' and D'. By cross-ratio invariance, we have

therefore,

Step 3: A, B, C and D are on the four calibration lines of the calibration board, so it can be obtained

Further available:

Step 4: Since the 4 calibration lines of the calibration board are coplanar, the z coordinate of the spatial coordinates of the target board is , which can be set according to the needs, and the (x, y, z) coordinates of point D can be obtained.

4. The homography matrix H formula from the target point to the imaging point can calculate the corresponding H matrix

The 4-line calibration board in the step (1), the 4 lines meet the following rules: , , , , It can be set according to the requirement.

Step 1: From the general line scan camera homography formula

Deriving the homography formula of linear single-array camera

is the scale parameter;

So the homography matrix H is

Step 2: According to the homography formula of the ordinary line array camera, according to the target point (x, y, z) and the corresponding imaging point coordinate d(u), the zero coordinate point of the imaging coordinate is the vertex in the da direction, and the homography can be calculated Responsive matrix H.

In order to verify the effectiveness of the present invention, a line scan camera model of DALSA Piranha series P2-2x-04K30 with a resolution of 1×4096 and a pixel size of 7 μm was used. Calibration board 4 line parameters mm, the z-axis coordinate of the calibration plate space is zero.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than limit them. Although the embodiments have described the present invention in detail, those of ordinary skill in the art should understand that modifications or equivalent replacements to the technical solutions of the present invention do not depart from the spirit and scope of the technical solutions of the present invention, and all of them should be included in the scope of the present invention. within the scope of the claim.

Claims (4)

1. A calculation method of a single line array camera homography matrix H, characterized in that: the steps of the method are as follows: (1) Use the Hough calculation method to extract the lines in the image of the single-line array camera, take any line in the line in the image plane, intersect this line with the 4 lines in the image of the 4-line calibration plate captured, and take the intersection points as a, b, c and d; 4-line calibration board, 4 lines meet the following rules: D1:y=0, D2:y=α, D3:y=2α, D4:y=x+3α, α can be customized according to the demand set up; (2) Calculate the cross-ratio CR(a,b; c,d) of imaging points a, b, c and d; (3) Using cross-ratio invariance to obtain the cross-ratio CR (A, B; C, D) of imaging points a, b, c, and d corresponding to target points A, B, C, and D, and then calculate point D (x, y, z) coordinates; Among them, the calculation steps of the (x, y, z) coordinates of point D are as follows: Step 1. A virtual line D5, which is parallel and coplanar with D1, D2, D3, D1, D2, D3 and passing through D point D5, these four parallel lines intersect with the y-axis at A', B', C' and D' , with cross-ratio invariance, CR(A,B; C,D)=CR(A',B';C',D'); Step 2, A, B, C and D are on the four calibration lines of the calibration board, so it can be obtained $\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; /</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; /</span>\frac{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}$ Further available: $\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}$ $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; )</span>}{\mathrm{<span\; class="notranslate">\; r</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 3</span>}\mathrm{<span\; class="notranslate">\; \&alpha;</span>}$ Since the 4 calibration lines of the calibration plate are coplanar, the z coordinate of the spatial coordinates of the target plate is β, which can be set according to the needs, and the coordinates of point D (x, y, z) can be obtained; (4) Substitute point D and the corresponding imaging point coordinates of point D into the homography matrix H formula from the target point to the imaging point, and the corresponding H matrix can be calculated. 2. the computing method of a kind of single line array camera homography matrix H according to claim 1, is characterized in that: the intersection ratio of four points a, b, c and d on the straight line in the described step (2) is ac is the distance between a and c, bc is the distance between b and c, ad is the distance between a and d, and bd is the distance between b and d. 3. the calculation method of a kind of single line array camera homography matrix H according to claim 1, is characterized in that: in the described step (3), cross-ratio invariance is CR (A, B; C, D)= CR(a,b;c,d). 4. the calculation method of a kind of single line array camera homography matrix H according to claim 1, is characterized in that: the step of calculating homography matrix H in the described step (4) is as follows: Step 1. From the homography formula of ordinary line scan camera $\mathrm{<span\; class="notranslate">\; the\; s</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; u</span>}\\ \mathrm{<span\; class="notranslate">\; v</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 41</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 12</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; two</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 32</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 42</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \mathrm{<span\; class="notranslate">\; z</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ Deriving the homography formula of linear single-array camera $\mathrm{<span\; class="notranslate">\; the\; s</span>}\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; u</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]<span\; class="notranslate">\; =</span>\left[\begin{array}{cccc}{\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 11</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; one</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 31</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 41</span>}}\\ {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 13</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; twenty\; three</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 33</span>}}& {\mathrm{<span\; class="notranslate">\; h</span>}}_{\mathrm{<span\; class="notranslate">\; 43</span>}}\end{array}\right]\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; x</span>}\\ \mathrm{<span\; class="notranslate">\; the\; y</span>}\\ \mathrm{<span\; class="notranslate">\; z</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}\end{array}\right]$ s is the scale parameter; So the homography matrix H is Step 2. According to the homography formula of the ordinary line array camera, according to the target point D(x, y, z) and the corresponding imaging point coordinate d(u), the zero coordinate point of the imaging coordinate is the vertex in the da direction, and it can be calculated The homography matrix H.