A fast homography estimation method with geometric significance

Abstract

The embodiment of the present invention relates to a fast homography estimation method with geometric meaning, comprising the following steps: extracting corresponding feature point pairs between images; selecting two points from the obtained point pairs as double anchor point pairs of each image, respectively, obtaining the similarity transformation matrix of each of the two images, and performing a two-dimensional similarity transformation on other points in each image; for multiple point pairs other than the double anchor points, using the cotangent value of the angle and the cross ratio to obtain the kernel transformation matrix between the two planes after the similarity transformation. The present invention can significantly shorten the time spent on calculating the homography matrix for four or more points, and avoid the problem that the estimated parameters have no geometric meaning.

Description

Technical Field

[0001] The invention relates to the technical field of computer vision, and in particular to a fast and geometrically meaningful homography matrix estimation method. Technical Background

[0002] Nowadays, with the continuous development of smart phones, we can easily obtain images from our surroundings, so computer vision is increasingly used in our lives. Among them, two-dimensional projective transformation, also known as planar homography, is a theoretical basis of computer vision, which describes the mapping relationship between a plane and the imaging surface under the perspective projection of the camera. Planar homography calculation is widely used in tasks such as panorama stitching, camera calibration, attitude estimation, visual synchronous positioning and mapping, and is a very common and important technology.

[0003] Researchers have proposed a variety of methods to solve the problem of calculating plane homography. For example, the Direct Linear Transformation (DLT) method uses four or more pairs of points that are completely matched between two planes to solve the homography, and has good robustness. However, the shortcomings of this algorithm are also obvious. It needs to calculate the SVD decomposition of the 9x9 matrix, which will result in a large amount of calculation and slow speed. Moreover, the SVD decomposition only decomposes the matrix into singular values, which has only algebraic meaning but no geometric meaning. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a fast and geometrically meaningful homography decomposition method, which can significantly shorten the time consumed in calculating the homography matrix of four or n points and avoid the problem that the estimated parameters lack geometric meaning.

[0005] The technical solution adopted by the present invention to solve the technical problem is to provide a fast and geometrically meaningful homography decomposition method, comprising the following steps:

[0006] (1) Extract corresponding feature point pairs between images or between template and image;

[0007] (2) Select two points from the obtained point pairs as the double anchor point pairs of each image and calculate their The transformation of two similarity transformation matrices H s1 , H s2 , and use the corresponding similarity transformation matrix to perform a two-dimensional similarity transformation on the remaining feature points in each image;

[0008] (3) In the case of four points, the third and fourth point pairs other than the double anchor points are selected, and the kernel transformation matrix H between the two planes after similarity transformation is obtained using linear constraints. k ;

[0009] (4) In the case of multiple points, (n-2) points are used to optimize and solve the kernel transformation matrix in step (3).

[0010] The cotangent value and cross ratio of the angle formed by the two anchor points and the additional third point are used to represent the geometric meaning of each parameter of the kernel transformation matrix proposed in step (3).

[0011] In step (2) of the present invention, when selecting dual anchor points, selecting two points with the longest distance as dual anchor points can increase the robustness of the algorithm and suppress the influence of image noise.

[0012] Due to the adoption of the above technical solution, the present invention has the following advantages and positive effects compared with the prior art: the present invention no longer uses the traditional method of direct linear transformation to realize the plane homography estimation, which can avoid the SVD decomposition process with large amount of calculation and only algebraic significance. The present invention decomposes the homography matrix into the multiplication form of three simple matrices, which can greatly accelerate the homography estimation in the case of four or more points. In particular, the present invention can use (n-2) point pairs to obtain the optimal solution of the kernel transformation matrix, which gives each parameter geometric meaning while improving the robustness of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic diagram of the three-part decomposition when estimating the planar homography between two images.

[0014] Figure 2 It is a schematic diagram of the transformation effect of the kernel transformation matrix between two planes and each of its parameters after two similarity transformations. DETAILED DESCRIPTION

[0015] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0016] The embodiment of the present invention relates to a fast homography estimation method with geometric significance, comprising the following steps: (1) extracting corresponding feature point pairs between images; (2) selecting two points from the obtained point pairs as double anchor point pairs of each image, and calculating their correspondence to The transformation of two similarity transformation matrices H s1 , H s2, and use the corresponding similarity transformation matrix to perform a two-dimensional similarity transformation on the remaining feature points in each image; (3) In the case of four points, for the third and fourth point pairs other than the double anchor points, linear constraints are used to find the kernel transformation matrix H between the two similarity transformed planes. k (4) In the case of multiple points, use (n-2) points to optimize and solve the kernel transformation matrix in step (3).

[0017] The following example uses 4 point pairs to calculate the homography H between two planes (see Figure 1 ), specifically explain the method provided by this method, a fast and geometrically meaningful homography decomposition method. The geometric meaning of the kernel similarity transformation is as follows Figure 2 As shown, They represent the infinite points on the x-axis and y-axis on the plane π3, respectively. represents the point with coordinates (0,1,1) on plane π3, is the point after the above three points are transformed to plane π4 by kernel transformation. The specific steps are:

[0018] Step 1: Extract 4 corresponding feature point pairs between two planes π1 and π2, denoted as Where X refers to Figure 1 One of the four coplanar points N, M, P, Q shown in ; the subscript indicates the plane number.

[0019] Step 2: Select two feature points M1 and N1 from plane π1 as double anchor points. Use the linear equations to solve a specific two-dimensional similarity transformation matrix H s1 , so that M1, N1 through H s1 Translate, rotate, and scale points into homogeneous coordinate pairs Let the midpoint of these two points be the origin of the coordinate system O, and π1 is also at H s1 The effect is changed to plane π3, and H is also used for the remaining points P1 and Q1 s1 The corresponding points P3, Q3 on plane π3 are obtained by translation, rotation and scaling calculations.

[0020] Step 3: Similarly, perform the same operation on the feature points M2 and N2 on plane π2 to calculate the similarity transformation matrix H s2 Similarly, make M2, N2 pass through H s2 Transform to homogeneous coordinate point pair π2 is also in H s2 The effect of H is transformed into plane π4, and the remaining points P2 and Q2 are also s2 Transformed to point P4,Q4.

[0021] Step 4: For the obtained plane π3, we can use the four unknowns a K ,bK ,u K ,v K The kernel transformation matrix H k Convert it to plane π4. Specifically, using the corresponding point pair and Constructing a homogeneous linear equation system of point transformations can solve H k .

[0022]

[0023] Multiply the three obtained matrices to obtain the original homography So far, a fast homography matrix decomposition calculation method for four corresponding feature point pairs has been proposed. K Each parameter in has a clear geometric meaning (see Figure 2 ), and the point transformation process explicitly represents the projective invariant calculation process of the intersection ratio of the co-point line bundles at the double anchor points. Using this property, we can get the H calculation of the remaining n-2 points excluding the double anchor points in the case of n points. K The estimated optimal solution is as follows:

[0024] Step S1: Use algebraic error to represent the residual function in

[0025]

[0026]

[0027] The known quantity Represents the i-th feature point on plane π3 and π4 respectively and (excluding the double anchor point number) and the cotangent value of the angle between the double anchor points, such as Here, the suffixes .x and .y represent the x-axis and y-axis coordinate values ​​of this point respectively.

[0028] Step S2: Use the least squares method to solve the above equation.

[0029]

[0030] Step S3: The above solution under algebraic error can be further expanded into the following form, where represents the average of (n-2) x values,

[0031]

[0032] Step S4: Or write a second residual function based on the residual function in step 1 The three known quantities can be calculated from the coordinate values ​​of the corresponding point pairs:

[0033] Step S5: Calculate the residual function F2 The partial derivative of

[0034]

[0035] Step S6: Indicates The sum of the products of each coefficient in

[0036]

[0037] Step S7: Find

[0038]

[0039] Step S8: Replace the "+" in step 1 with "-" and repeat the following steps to find

[0040] So far, (n-2) point pairs other than the double anchor points have been used to estimate the kernel transformation matrix H k The optimized solution of can be further used to find the complete homography H.

[0041] Through experiments and analysis, it is found that the method of the present invention is faster than the previous methods. The theoretical analysis of floating point calculations and the actual experimental test can speed up the classical DLT method by 10-100 times (increases according to the number of points). In addition, it is also found that the selection of double anchor points also affects the robustness of the method proposed by the present invention. When the double anchor points are selected randomly and multiple times, the method has better robustness.

Claims

1. A fast and geometrically meaningful homography decomposition method, characterized in that: The following steps are involved: (1) Extract corresponding feature point pairs between images or between template and image; (2) Select two points from the obtained point pairs as the double anchor point pairs of each image and calculate their The transformation of two similarity transformation matrices H s1 , H s2 , and use the corresponding similarity transformation matrix to perform a two-dimensional similarity transformation on the remaining feature points in each image; (3) In the case of four points, select the third and fourth point pairs other than the double anchor points from the corresponding feature point pairs to find the kernel transformation matrix H between the two planes after similarity transformation. k ; (4) In the case of multiple points, (n-2) points are used to optimize and solve the kernel transformation matrix in step (3); The specific process is: Step 1: Use algebraic error to express the residual function in The known quantity Represents the i-th feature point on plane π3 and π4 respectively and The cotangent value of the angle between the two anchor points, Here, the suffixes .x and .y represent the x-axis and y-axis coordinate values ​​of this point respectively; Step 2: Use the least squares method to solve the above equation. in is the coefficient matrix; Step 3: The above solution under algebraic error is further expanded to the following form, where represents the average of (n-2) x values, Step 4: Write a second residual function based on the residual function in step 1 The three known quantities can be calculated from the coordinate values ​​of the corresponding point pairs: Step 5: Calculate the residual function F2 The partial derivative of Step 6: Show The sum of the products of each coefficient in Step 7: Find Step 8: Replace the "+" in step 1 with "-" and repeat the following steps to find So far, (n-2) point pairs other than the double anchor points have been used to estimate the kernel transformation matrix H k Optimized solution.

2. The fast and geometrically meaningful homography decomposition method according to claim 1, characterized in that: The geometric meaning of each parameter of the kernel transformation matrix proposed in step (3) is represented by the cotangent value and the cross ratio of the angle between the anchor line formed between the two anchor points and the co-point line formed by one anchor point and an additional third point.

3. The fast and geometrically meaningful homography decomposition method according to claim 1, characterized in that: When selecting dual anchor points in step (2), selecting the two points with the longest distance as dual anchor points can increase the robustness of the algorithm and suppress the influence of image noise.

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