A method for reducing feature point mismatch rate based on matrix eigenvalues

Abstract

This invention provides a method for reducing feature point mismatch rates based on matrix eigenvalues, belonging to the field of visual target pose measurement system design. The method includes the following steps: defining a projection process from 3D world coordinates to 2D image coordinates, initializing all matching points as correct points, using the correct points to convert a nonlinear system into a linear system and defining an error function, predicting the 2D image coordinates, obtaining the error between the predicted and measured image coordinates, analyzing the error distribution to determine erroneous and correct points, and repeating the above process several times based on the selected correct points, thereby continuously reducing the feature point mismatch rate. This invention reduces the feature point mismatch rate through batch processing of erroneous points.

Description

Technical Field

[0001] This invention belongs to the field of visual target localization system design, and specifically relates to a method for reducing feature point mismatch rate based on matrix eigenvalues. Background Technology

[0002] Currently, vision-based relative measurement involves determining the pose and position of a target. Considering the applications of visual pose measurement technology in many fields such as robotics and spacecraft navigation, numerous pose calculation methods have been proposed. Typically, a target contains many feature points, and the pose measurement scheme can be transformed into a perspective feature point pose calculation problem. This involves the correspondence between 3D point coordinates and 2D image projections. However, due to characteristics such as illumination and shadows, feature point mismatches can occur during image processing. The presence of mismatched points introduces estimation errors into the pose calculation algorithm; generally, the higher the mismatch rate, the greater the error. Therefore, how to reduce the feature point mismatch rate to serve accurate target pose measurement is a pressing problem in the field of visual relative measurement engineering. Summary of the Invention

[0003] In practical visual target localization tasks, the error in target localization can be increased due to the mismatch problem introduced by image processing algorithms. This invention provides a method for reducing the feature point mismatch rate based on feature values. By batch processing the erroneous points, the feature point mismatch rate can be reduced.

[0004] To achieve the above objectives, the present invention provides a method for reducing feature point mismatch rate based on matrix eigenvalues, characterized by comprising the following steps:

[0005] Step S1: Define the process of projecting 3D world coordinates to 2D image coordinates, and initialize all matching points as correct points;

[0006] Step S2: Use the correct points to convert the nonlinear system into a linear system and define an error function to predict the coordinates of the two-dimensional image;

[0007] Step S3: Obtain the error between the image coordinates of the predicted and measured values, and determine the error points and correct points by analyzing the error distribution;

[0008] Step S4: Based on the selected correct points, repeat steps S2 and S3 several times to continuously reduce the feature point mismatch rate.

[0009] Furthermore, in step S1, for the three-dimensional world coordinate point P... i =[P i x ,P i y ,Pi z ,1] T To the two-dimensional image coordinates p i =[u i ,v i ,1] T The perspective process of projection is as follows:

[0010] s i p i =K[R|t]P i (1)

[0011] Among them, s i Let K represent the depth of the i-th point, K represent the known camera internal calibration parameters, and R and t represent the rotation matrix and position vector, respectively.

[0012]

[0013] The matrix is ​​defined as follows:

[0014]

[0015] Further, step S2 specifically includes:

[0016] Rewrite the H matrix in formula (3) as a vector h:

[0017] h = [r 11 ,r 21 ,r 31 ,t1,r 12 ,r 22 ,r 32 ,t2,r 13 ,r 23 ,r 33 ,t3] T (3)

[0018] Given n pairs of three-dimensional world coordinate points {P i =[P i x ,P i y ,P i z ,1] T} i＝1,...,n To the two-dimensional image coordinates {p i =[u i ,v i ,1] T} i＝1,...,n Then, using direct linear transformation, we derive formula (1) as follows:

[0019] Mh=0 9×1 (4)

[0020]

[0021] Among them 0 i×j The zero matrix representing i times j is decomposed into two matrices M based on the image coordinates u and v, respectively. u M v :

[0022]

[0023] First, use M u The matrix defines an error function based on eigenvalues:

[0024]

[0025] in The image coordinates to be predicted are: symbol Let f(x) represent the value of variable x that minimizes f(x), and det(x) represent the determinant of matrix x. Let:

[0026]

[0027] in Representative matrix Z u The matrix formed by rows i to j and columns p to q, then And the analysis yielded

[0028] The above formula is derived as follows:

[0029]

[0030] Analysis reveals that the above formula is based on a concept... Find the minimum value of the square of a quadratic equation in one variable, and calculate the discriminant of a linear equation in two variables as follows:

[0031]

[0032] If Δ u If ≤0, then the solution to the error function in formula (7) is: If Δ u If >0, then the solution to the error function in formula (7) is:

[0033] Secondly, use M v The matrix defines another error function based on eigenvalues:

[0034]

[0035] in Let the predicted coordinates of the image be defined. And define:

[0036]

[0037] in Representative matrix Z v The matrix formed by rows i to j and columns p to q, then And the analysis yielded The following is derived from formula (7):

[0038]

[0039] Analysis shows that the above formula is based on a concept... Find the minimum value of the square of a quadratic equation in one variable, and calculate the discriminant of a linear equation in two variables as follows:

[0040]

[0041] If Δ v If ≤0, then the solution to the error function in formula (11) is: If Δ v If the value is greater than 0, then the solution to the error function in formula (11) is:

[0042] Furthermore, step S3 specifically includes:

[0043] Combination and Obtain the offset sequence and And defined as follows and The corresponding distance errors

[0044]

[0045] Where σ u It is composed of error sequences The calculated standard deviation, σ v It is composed of error sequences The calculated standard deviation. Using a set threshold δ, if the i-th point simultaneously meets the condition... and If it is a correct point, it is considered a correct point; otherwise, it is considered an incorrect point. Finally, the sequence {P} is considered correct. i} i＝1,...,n and {p i} i＝1,...,n Select the correct point from the list.

[0046] Furthermore, in step S4, matrix M is reconstructed using the correct points from step S2. u and M v Perform the above S2 and S3 operations, set the number of iterations, and update the threshold δ by multiplying the threshold δ by the reduction factor ρ in each iteration, so as to continuously reduce the false matching rate based on the matrix eigenvalues.

[0047] The beneficial effects of this invention are:

[0048] 1) This invention takes into account the error distribution of erroneous and correct points and designs a method for reducing the feature point error matching rate based on matrix eigenvalues;

[0049] 2) This method avoids the pose calculation method in traditional feature point error matching and simplifies the feature point error matching process. Attached Figure Description

[0050] Figure 1 This is a flowchart of the feature point error matching rate reduction method based on matrix eigenvalues ​​according to an embodiment of the present invention;

[0051] Figure 2 This is a schematic diagram of a camera projection model according to an embodiment of the present invention;

[0052] Figure 3 Simulations were conducted to reduce the feature point mismatch rate in embodiments of the present invention. Detailed Implementation

[0053] The present invention will be further described below with reference to the accompanying drawings and embodiments. It should be understood that the embodiments described below are intended to facilitate the understanding of the present invention and are not intended to limit it in any way.

[0054] like Figure 1 As shown in this embodiment, a method for reducing feature point mismatch rate based on matrix eigenvalues ​​includes the following steps:

[0055] S1: Perform initialization, define the projection process from 3D world coordinates to 2D pixel coordinates, and define all matching points as correct points. Specifically, this includes:

[0056] Set the camera intrinsic parameter matrix K to be the identity matrix I. 3×3 For a feature point P in the three-dimensional world i =[P i x ,P i y ,P i z ,1] T Satisfying condition P i x ∈[-2,2],P i y∈[-2,2],P i z ∈[-2,2], rotation matrix R is arbitrarily given, position vector is set to [0.1,0.1,6] T The coordinates p of a two-dimensional image can be obtained using the principle of camera projection. i =[u i ,v i ,1] T Set 150 correct matching points {P} i} i＝1,...,150 and {p i =[u i ,v i ,1] T} i＝1,...,150 If the number of incorrect matching points is set to 150, the incorrect matching rate is 50%. The rules for generating incorrect matching points are as follows: 3D world feature points Still meets the conditions However, the corresponding p j =[u j ,v j ,1] T Conditions met:

[0057] u j ∈[min{u i ,i=1,...,150},max{u i ,i=1,...,150}]

[0058] and

[0059] v j ∈[min{v i ,i=1,...,150},max{v i ,i=1,...,150}]

[0060] For a feature point P in the three-dimensional world i =[P i x ,P i y ,P i z ,1] T To the two-dimensional image coordinates p i =[u i ,v i ,1] T The perspective process of projection is as follows Figure 2 As shown, specifically, coordinate system O w -X w Y w Z w For the world coordinate system, O c -Xc Y c Z c The camera reference coordinate system is defined, and the projection process is as follows:

[0061] s i p i =K[R|t]P i (1)

[0062] Among them, s i Let K represent the depth of the i-th point, K represent the known camera internal calibration parameters, and R and t represent the rotation matrix and position vector, respectively.

[0063]

[0064] The matrix is ​​defined as follows:

[0065]

[0066] Initialize 300 pairs of feature points to match the correct points.

[0067] Step S2: Using the correct points, transform the nonlinear system into a linear system and define an error function to predict the pixel coordinates of the two-dimensional pixels, specifically including:

[0068] Rewrite the H matrix in formula (3) as a vector h:

[0069] h = [r 11 ,r 21 ,r 31 ,t1,r 12 ,r 22 ,r 32 ,t2,r 13 ,r 23 ,r 33 ,t3] T (3)

[0070] Given 300 pairs of three-dimensional world coordinate points {P=[P i x ,P i y ,P i z ,1] T} i＝1,...,300 To the two-dimensional image coordinates {p i =[u i ,v i ,1] T} i＝1,...,300 Then, using direct linear transformation, we derive formula (1) as follows:

[0071] Mh=0 9×1 (4)

[0072] Where M consists of correctly matched points, as shown below:

[0073]

[0074] Among them 0 i×j The zero matrix representing i multiplied by j is decomposed into two matrices M based on the image coordinates u and v. u M v :

[0075]

[0076] First, use M u The matrix defines an error function based on eigenvalues:

[0077]

[0078] in Let be the predicted value of the image to be determined. symbol Let f(x) represent the value of variable x that minimizes f(x), and det(x) represent the determinant of matrix x. Let:

[0079]

[0080] in Representative matrix Z u The matrix formed by rows i to j and columns p to q, then And the analysis yielded The above formula is derived as follows:

[0081]

[0082] Analysis shows that the above formula is based on a concept... Find the minimum value of the square of a quadratic equation in one variable, and calculate the discriminant of a linear equation in two variables as follows:

[0083]

[0084] If Δ u If ≤0, then the solution to the error function in formula (7) is: If Δ u If >0, then the solution to the error function in formula (7) is:

[0085] Secondly, use M v The matrix defines another error function based on eigenvalues:

[0086]

[0087] in Let the predicted value of the image be defined. have to:

[0088]

[0089] in Representative matrix Z v The matrix formed by rows i to j and columns p to q, then And the analysis yielded The following is derived from formula (7):

[0090]

[0091] Analysis shows that the above formula is based on a concept... Find the minimum value of the square of a quadratic equation in one variable, and calculate the discriminant of a linear equation in two variables as follows:

[0092]

[0093] If Δ v If ≤0, then the solution to the error function in formula (11) is: If Δ v If the value is greater than 0, then the solution to the error function in formula (11) is:

[0094] Step S3: Obtain the error between the predicted and measured pixel coordinates. By analyzing the error distribution, determine the error points and correct points. Specifically, this includes:

[0095] Combination and Obtain the error sequence and And defined as follows and The corresponding distance errors

[0096]

[0097] Where σ u It is composed of error sequences The calculated standard deviation, σ v It is composed of error sequences The calculated standard deviation. Given a threshold δ = 3, if the i-th point simultaneously satisfies the condition... and If it is a correct point, then it is considered a correct point; otherwise, it is considered an incorrect point. Ultimately, this can be achieved by analyzing the sequence {P}. i ,P j} and {p i ,pj Select the correct point from the list.

[0098] Step S4: Reconstruct matrix M using the correct points from step S2. u and M v Perform the above S2 and S3 operations, and use step S3 to reselect the correct point. Set the number of loops to 30, and update the threshold δ by multiplying the threshold δ by the reduction factor ρ = 0.9 in each loop. Finally, the error matching rate is continuously reduced based on the matrix eigenvalue.

[0099] The simulation results of the feature point mismatch rate reduction method obtained by the method in this embodiment are as follows: Figure 3 As shown. Figure 3 It can be seen that as the number of iterations increases, the feature point mismatch rate decreases and the success rate increases.

[0100] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

[0101] For those skilled in the art, various modifications and improvements can be made to the embodiments of the present invention without departing from the inventive concept of the present invention, and these modifications and improvements all fall within the protection scope of the present invention.

Claims

1. A method for reducing feature point mismatch rate based on matrix eigenvalues, characterized in that, Includes the following steps: Step S1: Define the process of projecting 3D world coordinates to 2D image coordinates, and initialize all matching points as correct points; in step S1, for 3D world coordinate points... To two-dimensional image coordinates The perspective process of projection is as follows: （1） in, Indicates the first Depth of each point This indicates that the internal calibration parameters of the camera are known. and These are the rotation matrix and the position vector, respectively: （2） The matrix is ​​defined as follows: （3） Step S2: Using the correct points, transform the nonlinear system into a linear system and define an error function to predict the coordinates of the two-dimensional image, including: Formula (3) Matrix as a vector form: ； It is known that For three-dimensional world coordinate points To two-dimensional image coordinates Then, using direct linear transformation, we derive formula (1) as follows: （4） （5） in represent take The zero matrix, respectively based on the image coordinates and matrix Decomposed into two matrices : （6） First use The matrix defines an error function based on eigenvalues: （7） in The image coordinates to be predicted are: ,symbol Representative Variables that reach minimum value The value of , Representative matrix The determinant is set as follows: （8） in Representative matrix No. arrive line, number arrive A matrix composed of columns, then And the analysis yielded The above formula is derived as follows: （9） Analysis reveals that the above formula is based on a concept... Find the minimum value of the square of a quadratic equation in one variable, and calculate the discriminant of a linear equation in two variables as follows: （10） if Then the solution to the error function in formula (7) is ,if Then the solution to the error function in formula (7) is ; Secondly utilize The matrix defines another error function based on eigenvalues: （11） in Let the predicted coordinates of the image be defined. ,set up: （12） in Representative matrix No. arrive line, number arrive A matrix composed of columns, then And the analysis yielded The following is derived from formula (7): （13） Analysis shows that the above formula is based on a concept... Find the minimum value of the square of a quadratic equation in one variable, and calculate the discriminant of a linear equation in two variables as follows: （14） if Then the solution of the error function in formula (11) is ,if Then the solution of the error function in formula (11) is ; Step S3: Obtain the error between the image coordinates of the predicted and measured values, and determine the error points and correct points by analyzing the error distribution; Step S4: Based on the selected correct points, repeat steps S2 and S3 several times to continuously reduce the feature point mismatch rate.

2. The method for reducing feature point mismatch rate based on matrix eigenvalues ​​according to claim 1, characterized in that, Step S3 specifically includes: Combination and Obtain the offset sequence and and defined as follows and The corresponding distance errors : （15） in It is composed of error sequences The calculated standard deviation, It is composed of error sequences The calculated standard deviation is then used with a set threshold. If the first All points simultaneously meet the conditions and If the value is true, it is considered a correct point; otherwise, it is considered an incorrect point. Ultimately, the sequence is determined... and Select the correct point from the list.

3. The method for reducing feature point mismatch rate based on matrix eigenvalues ​​according to claim 2, characterized in that, In step S4, the matrix is ​​reconstructed using the correct points from step S2. and Perform the above S2 and S3 operations, set the number of iterations, and pass the threshold in each iteration. Multiply by the reduction factor Update threshold Ultimately, this leads to a continuous reduction in the false matching rate based on matrix eigenvalues.

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