A method for calculating target homography matrix based on consistent sampling algorithm

Abstract

The present invention discloses a target homography matrix calculation method based on a consistent sampling algorithm, and the steps are as follows: (1) designing a reasonable target; (2) screening target points for non-three-point collinearity, constructing a homography matrix equation and an overdetermined equation, and solving the H matrix parameters by the least square method; (3) calculating the error between the predicted value and the true value by the mean square error of the square cost function, and dividing the i-th point into an inner point set or an outer point set according to a threshold k; (4) according to whether the outer point obeys a Gaussian distribution, the standard normal distribution N~(0,1) is set, then its mean is 0 and the variance is σ; the degree of deviation between the theoretical threshold and the actual threshold is the residual conforming to the n-dimensional χ 2 The chi-squared one-sided independence test is used to obtain the threshold k; (5) the mean square error of the square cost function is less than the threshold k, and the optimal homography matrix is ​​obtained. The present invention can realize the rapid extraction of effective target points and eliminate the influence of invalid matching points on solving the homography matrix.

Description

Technical Field

[0001] The present invention relates to the technical field of camera calibration, and in particular to a method for calculating a target homography matrix based on a consistent sampling algorithm. Background Art

[0002] The homography matrix plays a very important role in computer vision fields such as image correction, image stitching, camera calibration and visual SLAM (Simultaneous Localization and Mapping). The homography matrix is ​​the mapping transformation relationship matrix from the two-dimensional world coordinate system to the three-dimensional image coordinate system. Its quality determines the calculation results in the corresponding application field.

[0003] Camera calibration establishes a correspondence between the 3D world and the camera imaging plane. This mapping relationship is reflected by the homography matrix. The accuracy of the homography matrix directly affects the accuracy of the camera's intrinsic parameters, extrinsic parameters, and images.

[0004] Zhang Zhengyou's plane calibration method uses chessboard points as the calibration template. However, this plane calibration method uses too many calibration points, so there are many error sources in the calibration point detection and matching process.

[0005] After searching, Chinese patent number ZL2016109183420 discloses a high-precision dynamic camera calibration method; the application uses a template image matching method to determine the checkerboard target area in the calibration image, and uses a checkerboard X-shaped calibration point detection method to remove the checkerboard calibration points and noise points with large edge distortion; based on the Gaussian surface optimization algorithm, the positioning accuracy of the checkerboard target X-shaped calibration points is improved; the camera calibration method based on non-measurement distortion correction is used to realize camera calibration, and the distortion model and distortion coefficient optimization model are introduced to improve the camera calibration accuracy; finally, the dynamic calibration of the camera is completed through the collected sequence images of the planar motion target, and the optimal homography matrix H corresponding to the image coordinates and world coordinates of the planar motion image is determined; the entire calibration process of the application only needs to solve and optimize a single distortion coefficient, and the calibration accuracy is improved; but the application still has the problem of many calibration points and many error sources in the calibration point detection and matching process. Summary of the invention

[0006] 1. Technical problem to be solved by the invention

[0007] In view of the above-mentioned problems existing in the prior art, the present invention provides a method for calculating the target homography matrix based on a consistent sampling algorithm; the present invention is a method for obtaining the homography matrix obtained by multiplying the camera intrinsic parameter matrix and the extrinsic parameter matrix, which can realize the rapid extraction of effective target points and eliminate the influence of invalid matching points on solving the homography matrix.

[0008] 2. Technical solution

[0009] In order to achieve the above object, the technical solution provided by the present invention is:

[0010] A target homography matrix calculation method based on a consistent sampling algorithm of the present invention comprises the following steps:

[0011] (1) Design a reasonable target;

[0012] (2) The homogeneous matrix equations are constructed by the pixel coordinates of the feature point image and the world coordinates to eliminate the mismatched points, and the target points are screened for non-collinear three points. The DLT direct linear transformation method is used to construct the homography matrix equation and the overdetermined equation, and the H matrix parameters are solved by the least squares method.

[0013] (3) The error between the predicted image pixel coordinates and the true value image pixel coordinates is calculated by the mean square error of the square cost function, and the i-th point is classified as belonging to the internal point set or the external point set according to the threshold k;

[0014] (4) According to the fact that the external points obey the Gaussian distribution, we set it to the standard normal distribution N~(0,1), then its mean is 0 and its variance is σ; the degree of deviation between the theoretical threshold and the actual threshold is the residual conforming to the n-dimensional χ 2 The characteristics of the distribution, the chi-square one-sided independence test was used to obtain the threshold k;

[0015] (5) The mean square error of the square cost function is less than the threshold k, and the optimal homography matrix is ​​obtained.

[0016] Furthermore, the number of target points n in step (1) is qualitatively analyzed and calculated by the RANSAC algorithm:

[0017]

[0018] Where w is the probability of the interior point, w n is the probability that the selected n points are all interior points, (1-w n ) k It represents the probability that not all n points are internal points after K repetitions, and p is the confidence level.

[0019] Furthermore, in step (1), the confidence level is set to p=0.95, and n is set to be the minimum matching number that satisfies the calculation of the homography matrix H, which is n=9, that is, the target is set to 9 points.

[0020] Furthermore, in step (2), 5 samples are randomly selected from the 9 target points designed in step (1) and it is ensured that the 5 samples are not collinear, specifically:

[0021] There are 10 constrained homography matrix equations for 5 feature points randomly selected from the target, in the form of:

[0022] AH=B

[0023] A is the coefficient matrix composed of the coordinate values ​​of the image coordinate system and the coordinate values ​​of the world coordinate system, and H is the homography matrix;

[0024] Determine whether the target points are collinear based on the solution of the nonlinear equations; the judgment criteria are:

[0025] (1) If R(A) = R(A|b) < 9, the nonlinear equation system is underdetermined, and the H matrix has nR(A) nonzero special solutions. Any linear combination of these nonzero special solutions is a solution of H. At this time, three of the five points of the target are collinear, making it a useless target.

[0026] (2) If R(A)=R(A|b)=9, the nonlinear equation system is overdetermined, and the target is a normal target, the H matrix can be obtained using 10 constrained homography matrix equations composed of 5 non-collinear feature points.

[0027] Furthermore, in step (2), the overdetermined equation uses the linear least squares method to calculate H and construct the Euclidean 2-norm The least squares solution is It is deduced that:

[0028] A T Ah=λh

[0029] h is the matrix A T The eigenvalue of A is the eigenvector of λ, and the Euclidean 2-norm is When the eigenvalue λ takes the minimum min hour, Minimum, then the least squares solution Yes A T A minimum eigenvalue λ min The corresponding eigenvector; eigenvalue λ min The corresponding eigenvectors form the H matrix.

[0030] Furthermore, in step (3), after removing three collinear points from the 9 points in the normal target, a set of 6 non-collinear points is screened out, which is recorded as M0; five non-collinear points are selected from M0, and the total The point set M'={M1,M2,M3,M4,M5} is composed of points. The least squares method of overdetermined equations is used to calculate the homography matrix H'={H1,H2,H3,H4,H5} corresponding to the point set M'={M1,M2,M3,M4,M5}. H' is called the temporary model parameter. The model H' is used to test the matching point set of the image pixel coordinate system and calculate the square error cost function:

[0031]

[0032]

[0033] k is the threshold, if Then the i point can be divided into the interior point set {Θ0}, if Then the i point can be divided into the external point set {Θ1}.

[0034] Furthermore, we propose the null hypothesis P0: "The threshold k is independent of the number of internal points". Based on the null hypothesis P0, the created classifier When the maximum value is obtained, Pearson χ 2 The calculation formula is: The chi-square value at this time It also takes a maximum value, indicating that the deviation between the theoretical threshold and the actual threshold is the largest, and the null hypothesis P0: "Threshold k is independent of the number of inliers" can be rejected; the alternative hypothesis P1: "Threshold k is related to the number of inliers" can be accepted, indicating that threshold k can most effectively distinguish inliers from outliers.

[0035] Furthermore, the threshold k is calculated as follows:

[0036] 1) The threshold k exists randomly in [0,n]. The threshold range is divided into two parts [0,k] and [k,n] by dichotomy. The two independent elements of the inner point and the outer point obtained by the dichotomy threshold are regarded as two degrees of freedom. It is judged whether the k value can significantly distinguish the inner point and the outer point, which is used as the standard for k to be the threshold; confirm the joint degrees of freedom, select the significance level α, and obey the chi-square distribution with a joint degree of freedom of 1. The corresponding chi-square distribution table Get the sampling data table;

[0037] 2) Calculate the theoretical expected values ​​α1, β1, α2, β2 of each row and column through the sampling data table;

[0038] 3) Due to the deviation of degrees of freedom, the calculation formula is corrected using Yates Find the chi-square value χ 2 ; Calculate E using the theoretical expected values ​​α1, β1, α2, β2 of each row and column i (i=1,2,3,4), calculate A using the observed frequencies of the internal and external points A1(k), A2(k), B1(k), B2(k) i (i=1,2,3,4);

[0039] 4) At different thresholds Select the largest It means that the deviation between the theoretical threshold and the actual threshold is the largest. The null hypothesis P0 can be rejected: "The threshold k is independent of the number of inliers"; the alternative hypothesis P1 can be accepted: "The threshold k is related to the number of inliers", which means that the threshold k can most effectively distinguish inliers from outliers. This is the optimal threshold k.

[0040] 3. Beneficial effects

[0041] Compared with the existing known technologies, the technical solution provided by the present invention has the following significant effects:

[0042] (1) The target homography matrix calculation method based on the consistent sampling algorithm of the present invention optimizes the circular target point selection and designs a target with 9 points, taking into account both the minimum matching number and the computational complexity of the homography matrix H. At the same time, the target points are screened for non-collinear three points and redundant points of collinear three points are eliminated, so that the effective target points can be quickly extracted and the influence of invalid matching points on solving the homography matrix is ​​eliminated.

[0043] (2) The present invention provides a method for calculating a target homography matrix based on a consistent sampling algorithm. The method uses the error of a square cost function to calculate the error between a predicted value and a true value of an image pixel coordinate system. The error is compared with a threshold k and classified into external points and internal points. The chi-square independence test is used to determine whether the threshold k can effectively distinguish between internal points and external points. The distinction between internal points and external points is more accurate, thereby improving the accuracy of the target homography matrix calculation. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of a target homography matrix calculation method based on a consistent sampling algorithm of the present invention;

[0045] Figure 2 It is a normal distribution internal and external point distribution diagram with a confidence level of 95% in the present invention;

[0046] Figure 3 A nine-point target diagram designed for;

[0047] Figure 4 Based on chi-square 2 Flowchart of the method for calculating the threshold k of the squared error cost function of the test. DETAILED DESCRIPTION

[0048] In order to further understand the content of the present invention, the present invention is described in detail in conjunction with the accompanying drawings and embodiments.

[0049] Example 1

[0050] In conjunction with the accompanying drawings, a target homography matrix calculation method based on a consistent sampling algorithm in this embodiment optimizes the circular target point selection, removes redundant points where three points are collinear, and obtains the homography matrix. In addition, a threshold value is reasonably designed to determine the square error cost function.

[0051] To achieve the above purpose, this embodiment includes the following steps:

[0052] Step 1: Design a reasonable target

[0053] Assume that the probability of each point being an inlier is w = number of inliers / (number of inliers + number of outliers). Usually we don’t know the exact value of w. n is the probability that the selected n points are all interior points, 1-w n is the probability that at least one of the n selected points is not an interior point, (1-w n ) k It indicates the probability that not all n points are internal points after K repetitions. Assume that the probability of success after the algorithm is executed K times is p. p is also called confidence, which indicates the degree of belief of an individual in the truth of the proposition. The confidence is usually set in the range of [0.95, 0.99] in experience. In this embodiment, the confidence is p = 0.95, which means that there is a 95% probability that the algorithm will succeed after K times of execution. Use matlab to generate a binary normal distribution random point matrix and draw the 95% confidence ellipse area of ​​the sample data. Then we have Figure 2 Distribution diagram of internal and external points shown.

[0054] Qualitative analysis of n value, calculated by RANSAC algorithm formula:

[0055]

[0056] In this embodiment, n is the minimum matching number that satisfies the calculation of the homography matrix H, and n=9 can be taken, that is, the target takes 9 points. Considering that the H matrix has at most 9 independent variables, theoretically at most 9 points are needed to calculate the homography matrix H. K represents the number of experiments required to calculate the homography matrix H, and K is positively correlated with n. To simplify the computational complexity, the larger the value of n, the better. In this embodiment, n=9 is taken.

[0057] Step 2: Use the pixel coordinates of the circular target feature point image and the world coordinates to construct a homogeneous matrix equation group to eliminate mismatched points and perform non-collinear screening of target points. To obtain stable results, 5 samples are randomly selected from the matching data set, i.e., the 9 target points designed in step 1, and ensure that these 5 samples are not collinear. Specifically:

[0058] Let the coordinates of the 3D point of the spatial plane measurement target in the world coordinate system be [x i ,y i ,z i ] T , the corresponding 2D point coordinates in the image pixel coordinate system are [x i ',y i ',z i '] T , the mapping relationship between the two is expressed as:

[0059]

[0060] Among them, h ij(1≤i=j≤3,∈z) is the homography matrix component.

[0061]

[0062] U=[h 11 h 12 h 13 ] T , V = [h 21 h 22 h 23 ] T , W = [h 31 h 32 h 33 ] T , since it is a homogeneous coordinate system, we can let z′ i =z i =1.

[0063] Using the DLT direct linear transformation method, we can get the following by dividing the third line:

[0064]

[0065] Transform Written in matrix form:

[0066]

[0067] Know H T =[U T V T W T ]Let h T =[UVW], the above matrix is ​​rewritten as the equation for h consisting of unknown numbers U, V, W:

[0068]

[0069] Ab=0

[0070] That is, Ah=B

[0071] One feature point corresponds to two homography matrix equations, which are two constraints. Therefore, there are 10 constraint homography matrix equations for the five feature points randomly selected from the target. It can be written in the form of a matrix equation: AH = B, where A is the coefficient matrix composed of the coordinate values ​​of the image coordinate system and the coordinate values ​​of the world coordinate system, and H is the homography matrix. Whether the target points are collinear is determined based on the solution of the nonlinear equation system.

[0072] R(A) is the rank of the coefficient matrix A, and R(A|B) is the rank of the augmented matrix.

[0073] (1) If R(A) = R(A|B) < 9, the nonlinear equation system is underdetermined. The H matrix has nR(A) non-zero special solutions, and any linear combination of these non-zero special solutions is a solution of H. In this case, three of the five points of the target are collinear, making it a useless target.

[0074] (2) If R(A) = R(A|B) = 9, the nonlinear equation system is overdetermined. The target is a normal target, and the H matrix can be obtained using 10 constrained homography matrix equations composed of 5 non-collinear feature points.

[0075] The constraints of the target's five-point coordinates are greater than the number of unknowns in the H matrix. The H matrix can be calculated

[0076] Overdetermined equations use linear least squares to calculate H and construct the Euclidean 2-norm The least squares solution is Due to the invariance of the S scale factor, let the constraint norm ||H|| = t, and use the Lagrange multiplier method: First-order partial derivative

[0077]

[0078] L'(h)=2A T Ah-2λh=0

[0079] L'(λ)=th T h=0

[0080] The solution is: A T Ah=λh, that is, h is the matrix A T The eigenvalue of A is the eigenvector of λ, and the Euclidean 2-norm is When the eigenvalue λ takes the minimum min hour, Minimum, then the least squares solution Yes A T A minimum eigenvalue λ min The corresponding eigenvector. Eigenvalue λ min The corresponding eigenvectors form the H matrix.

[0081] Step 3: Calculate the error between the predicted value and the true value of the image pixel coordinate system through the mean square error of the square cost function, and divide the i-th point into the internal point set or the external point set according to the threshold k.

[0082] After removing the three collinear points {(x0,y0),(x3,y3),(x7,y7)} from the 9 points of the normal target in step 2, 6 non-collinear point sets are screened out, denoted as M0 = {(x1,y1),(x2,y2),(x4,y4),(x5,y5),(x6,y6),(x8,y8)}, and five non-collinear points are selected from M0. The point set M'={M1,M2,M3,M4,M5} is composed of , and the least squares method of the overdetermined equation in step 2 (2) is used to calculate the homography matrix H'={H1,H2,H3,H4,H5} corresponding to the point set M'={M1,M2,M3,M4,M5}. H' is called the temporary model parameter. Use the model H' to test the matching point set of the image pixel coordinate system and calculate the square error cost function:

[0083]

[0084]

[0085] k is the threshold, if Then the i point can be divided into the interior point set {Θ0}, if Then the i point can be divided into the external point set {Θ1}.

[0086] Step 4: Find the k threshold. Based on the fact that the outer points are Gaussian white noise, the central limit theorem shows that the inner and outer points obey the standard normal distribution N~(0,1), so its mean is 0 and its variance is σ. The degree of deviation between the theoretical threshold and the actual threshold is the residual conforming to the n-dimensional χ 2 The characteristics of the distribution, its probability density function is The threshold k is obtained by using the chi-square independence chi-square test to determine whether the threshold k can effectively distinguish between inliers and outliers. Create a classifier f: The threshold k can be divided into two sets of internal points and external points {Θ0} and {Θ1}. The internal point set {Θ0} represents The classifier is used to characterize the degree of deviation between the theoretical threshold and the actual threshold. A null hypothesis P0 can be proposed: "The threshold k is independent of the number of internal points". Under the condition that the null hypothesis P0 is established, the created classifier When the maximum value is obtained, Pearson χ 2 The calculation formula is: The chi-square value at this time When it also takes a maximum value, it means that the deviation between the theoretical threshold and the actual threshold is the largest, and the null hypothesis P0 can be rejected: "The threshold k is independent of the number of inliers" and the alternative hypothesis P1 can be accepted: "The threshold k is related to the number of inliers". This shows that the threshold k can most effectively distinguish inliers from outliers.

[0087] χ 2 Indicates the degree of deviation between the theoretical threshold and the actual threshold, A represents the observed frequency of the inner and outer points, E represents the expected frequency calculated based on P0, and the difference between A and E is the residual. The calculation process of the threshold k is as follows:

[0088] (1) Null hypothesis P0: "The threshold k is independent of the number of inliers", alternative hypothesis P1: "The threshold k is related to the number of inliers".

[0089] (2) The threshold k exists randomly in [0,n]. The threshold range is divided into two parts [0,k] and [k,n] by dichotomy, which are also regarded as two degrees of freedom. At the same time, the two independent elements of the inner point and the outer point obtained by the dichotomy threshold are also regarded as two degrees of freedom. It is judged whether the k value can significantly distinguish the inner point and the outer point as the standard for k as the threshold. Confirm that the joint degree of freedom is (2-1)×(2-1)=1. Select the significance level α=0.05, and obey the chi-square distribution with a joint degree of freedom of 1. The corresponding chi-square distribution table

[0090] There is a downsampling data table

[0091]

[0092] (3) Calculate the theoretical expected values ​​α1, β1, α2, β2 of each row and column respectively through the sampling data table:

[0093] The theoretical expected value of the number of outliers corresponding to the threshold range [0, k) is: Similarly, β1, α2, and β2 can also be calculated by the sum of the rows and the sum of the columns.

[0094]

[0095] (4) The two independent elements of the inner point and the outer point obtained by the binary threshold are also regarded as two degrees of freedom, and the combined degree of freedom is (2-1)×(2-1)=1. Since there is a deviation in the degree of freedom 1, the Yates correction calculation formula is used. Find the chi-square value χ 2 . Calculate E using the theoretical expected values ​​α1, β1, α2, β2 of each row and column i (i=1,2,3,4), calculate A using the observed frequencies of the internal and external points A1(k), A2(k), B1(k), B2(k) i (i=1,2,3,4).

[0096]

[0097] The total rows or columns of the chi-square table are summed up to:

[0098] (5) At different thresholds Select the largest It means that the deviation between the theoretical threshold and the actual threshold is the largest, and the null hypothesis P0 can be rejected: "The threshold k is independent of the number of inliers"; the alternative hypothesis P1: "The threshold k is related to the number of inliers" can be accepted. This means that the threshold k can most effectively distinguish inliers from outliers, and this is the optimal threshold k.

[0099] Step 5: Compare the minimum value of the squared error cost function with the optimal threshold k. If At this time the corresponding Composed of is the optimal homography matrix.

[0100]

[0101] The above is a schematic description of the present invention and its implementation methods, which is not restrictive. The drawings show only one implementation method of the present invention and are not limited thereto. Therefore, if a person skilled in the art is inspired by it and designs methods and embodiments similar to the technical solution without creativity without departing from the purpose of the invention, they should all fall within the scope of protection of the present invention.

Claims

1. A target homography matrix calculation method based on a consistent sampling algorithm, characterized in that: The steps are: (1) Design a reasonable target; specifically, qualitatively analyze the number of target points n and calculate it using the RANSAC algorithm: Where w is the probability of the interior point, w n is the probability that the selected n points are all interior points, (1-w n ) k It represents the probability that not all n points are inliers after K repetitions, and p is the confidence level. The confidence level is p=0.95, and n is the minimum matching number that satisfies the calculation of the homography matrix H, which is n=9, i.e., the target takes 9 points. (2) The homogeneous matrix equations are constructed by the pixel coordinates of the feature point image and the world coordinates to eliminate the mismatched points, and the target points are screened for non-collinear three points. The DLT direct linear transformation method is used to construct the homography matrix equation and the overdetermined equation, and the H matrix parameters are solved by the least squares method. Specifically, Randomly select 5 samples from the 9 target points designed in step (1) and ensure that the 5 samples are not collinear. Specifically: There are 10 constrained homography matrix equations for 5 feature points randomly selected from the target, in the form of: AH=B A is the coefficient matrix composed of the coordinate values ​​of the image coordinate system and the coordinate values ​​of the world coordinate system, and H is the homography matrix; Determine whether the target points are collinear based on the solution of the nonlinear equations; the judgment criteria are: 1) If R(A)=R(A|b)<9, the nonlinear equation system is underdetermined, and the H matrix has nR(A) non-zero special solutions. Any linear combination of these non-zero special solutions is a solution of H. At this time, three of the five points of the target are collinear, making it a useless target; 2) If R(A)=R(A|b)=9, the nonlinear equation system is an overdetermined equation, and the target is a normal target, the H matrix can be obtained using 10 constrained homography matrix equations composed of 5 non-collinear feature points; (3) The error between the predicted image pixel coordinates and the true value image pixel coordinates is calculated by the mean square error of the square cost function, and the i-th point is classified as belonging to the internal point set or the external point set according to the threshold k; specifically: After removing three collinear points from the 9 points in the normal target, a set of 6 non-collinear points is selected, which is recorded as M0; five non-collinear points are selected from M0, and the total The point set M'={M1,M2,M3,M4,M5} is composed of points. The least squares method of overdetermined equations is used to calculate the homography matrix H'={H1,H2,H3,H4,H5} corresponding to the point set M'={M1,M2,M3,M4,M5}. H' is called the temporary model parameter. The model H' is used to test the matching point set of the image pixel coordinate system and calculate the square error cost function: k is the threshold, if Then the i point can be divided into the interior point set {Θ0}, if Then the i point can be divided into the external point set {Θ1}; (4) According to the fact that the external points obey the Gaussian distribution, we set it to the standard normal distribution N~(0,1), then its mean is 0 and its variance is σ; the degree of deviation between the theoretical threshold and the actual threshold is the residual conforming to the n-dimensional χ 2 The characteristics of the distribution, the chi-square one-sided independence test was used to obtain the threshold k; (5) The mean square error of the square cost function is less than the threshold k, and the optimal homography matrix is ​​obtained.

2. The target homography matrix calculation method based on the consistent sampling algorithm according to claim 1 is characterized in that: In step (2), the overdetermined equation uses the linear least squares method to calculate H and construct the Euclidean 2-norm The least squares solution is It is deduced that: IN T Ah=λh h is the matrix A T The eigenvalue of A is the eigenvector of λ, and the Euclidean 2-norm is When the eigenvalue λ takes the minimum min hour, Minimum, then the least squares solution Yes A T A minimum eigenvalue λ min The corresponding eigenvector; eigenvalue λ min The corresponding eigenvectors form the H matrix.

3. The target homography matrix calculation method based on the consistent sampling algorithm according to claim 2 is characterized in that: Propose the null hypothesis P0: "The threshold k is independent of the number of internal points". Based on the null hypothesis P0, the classifier created When the maximum value is obtained, Pearson χ 2 The calculation formula is: The chi-square value at this time It also takes a maximum value, indicating that the deviation between the theoretical threshold and the actual threshold is the largest, and the null hypothesis P0: "the threshold k is independent of the number of inliers" can be rejected; the alternative hypothesis P1: "the threshold k is related to the number of inliers" can be accepted, indicating that the threshold k can most effectively distinguish inliers from outliers.

4. The target homography matrix calculation method based on the consistent sampling algorithm according to claim 3 is characterized by: The calculation process of the threshold k is as follows: 1) The threshold k exists randomly in [0,n]. The threshold range is divided into two parts [0,k] and [k,n] by dichotomy. The two independent elements of the inner point and the outer point obtained by the dichotomy threshold are regarded as two degrees of freedom. It is judged whether the k value can significantly distinguish the inner point and the outer point, which is used as the standard for k to be the threshold; confirm the joint degrees of freedom, select the significance level α, and obey the chi-square distribution with a joint degree of freedom of 1. The corresponding chi-square distribution table Get the sampling data table; 2) Calculate the theoretical expected values ​​α1, β1, α2, β2 of each row and column respectively through the sampling data table; 3) Due to the deviation of degrees of freedom, the calculation formula is corrected using Yates Find the chi-square value χ 2 ; Calculate E using the theoretical expected values ​​α1, β1, α2, β2 of each row and column i (i=1,2,3,4), calculate A using the observed frequencies of the internal and external points A1(k), A2(k), B1(k), B2(k) i (i=1,2,3,4); 4) At different thresholds k, Select the maximum max It means that the deviation between the theoretical threshold and the actual threshold is the largest. The null hypothesis P0: "Threshold k is independent of the number of inliers" can be rejected; the alternative hypothesis P1: "Threshold k is related to the number of inliers" can be accepted, indicating that threshold k can most effectively distinguish inliers from outliers, and this is the optimal threshold k.

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