Basic matrix fitting method based on residual ordering and sparsity constraints

Abstract

This invention proposes a basic matrix fitting method based on residual sorting and sparsity constraints. The fitting method generates an effective distance matrix for a dataset containing multiple model instances and a high proportion of outliers, specifically including the following steps: Step S1: Set the input data and the number of model instances. S Number of samplings M Step S2: By improving the algorithm AGS, sampling weights and information theory principles are used to select effective data, and then a subset of data is selected from the effective data to generate... M One model hypothesis; Step S3: Use the generated model hypothesis. M The model assumes calculation of the discrimination distance matrix; Step S4: Calculate the sparse distance matrix using information theory; Step S5: Apply parameters... S The class labels are obtained by performing spectral clustering; this invention can effectively combine the advantages of residual sorting and sparsity constraints, and can efficiently generate more accurate distance matrices for data containing multiple model instances and a high proportion of outliers.

Description

Technical Field

[0001] This invention relates to the field of computer vision technology, and in particular to a basic matrix fitting method based on residual sorting and sparsity constraints. Background Technology

[0002] Robust model estimation is an important research area in computer vision and artificial intelligence. It has been widely applied in computer vision and AI, such as feature-based image registration, pose estimation, multi-object tracking, PPS and FM signal estimation, and 3D motion segmentation. Robust model estimation refers to estimating model hypotheses for all model instances (i.e., structures) from input data, given a geometric model (e.g., fundamental matrices), and then grouping outliers and interiors belonging to different structures into different groups based on the estimated model hypotheses.

[0003] Spectral clustering-based algorithms first construct a distance matrix and then perform spectral clustering on it to group data points into different groups. These algorithms have shown good performance on several public test datasets, such as AdelaideRMF and Hopkins 155. There are two main methods for constructing the distance matrix: model estimation-based methods and non-model estimation-based methods. The former is more popular because it is less affected by missing data and is robust to outliers. To generate accurate model hypotheses, sampling algorithms for model estimation methods need to sample at least a clean minimum subset. A clean minimum subset consists of the minimum number of data points belonging to the same structure used to estimate the geometric model. Sampling algorithms can be divided into two types: random sampling algorithms and guided sampling algorithms. Random sampling was first used in RANSAC and remains widely used in many model estimation methods due to its simplicity. However, to sample a clean minimum subset using random sampling, the number of samples required grows exponentially as the dimension of the geometric model increases.

[0004] To mitigate the drawbacks of random sampling, numerous guided sampling algorithms have been proposed. Unlike random sampling, which assigns an equal sampling weight to each data point, guided sampling algorithms allocate sampling weights calculated from various sources (e.g., matching scores or preference analysis) to each data point. Guided sampling algorithms can be categorized into four types: spatial proximity-based, matching score-based, greedy search-based, and preference analysis-based algorithms.

[0005] Sampling algorithms based on residual ranking are among the most promising guided sampling algorithms because they excel at finding interior points belonging to the same model instance (i.e., structure). Algorithms based on preference analysis calculate sampling weights from the residual exponents of preference analysis.

[0006] Early residual-based sampling algorithms required calculating sampling weights for all input data (w-1) times to sample a subset of data with w data points. To improve computational efficiency, an algorithm was proposed to calculate sampling weights only for the portion excluding all input data using local constraints. However, this algorithm still required calculating sampling weights (w-1) times to sample the minimum subset. To further improve computational efficiency, an improved algorithm, AGS, was proposed. This algorithm selects effective data using sampling weights and information theory principles, and then selects a subset of data from the effective data. AGS only calculates sampling weights once for the sampled data subset. Experimental results show that AGS outperforms several guided sampling algorithms.

[0007] This invention proposes a solution to the aforementioned problems. First, it comprehensively analyzes and studies the latest literature on robust model estimation, including data sampling and model selection algorithms. Second, it proposes an effective robust model estimation method by selecting an effective preference analysis-based sampling algorithm to generate promising model hypotheses and calculate a discriminative distance matrix. Then, it uses information theory principles to obtain a more discriminative sparse distance matrix. Finally, it performs spectral clustering on the sparse distance matrix to accurately segment the data.

[0008] The sampling method proposed in this invention can be used in robust model fitting, and thus applied to feature-based image registration, pose estimation, multi-target tracking, PPS and FM signal estimation, and 3D motion segmentation. Summary of the Invention

[0009] This invention proposes a basic matrix fitting method based on residual sorting and sparsity constraints, which can effectively combine the advantages of residual sorting and sparsity constraints, and can efficiently generate more accurate distance matrices for data containing multiple model instances and a high proportion of outliers.

[0010] The present invention adopts the following technical solution.

[0011] A basic matrix fitting method based on residual sorting and sparsity constraints is used to generate an effective distance matrix for a dataset containing multiple model instances and a high proportion of outliers. The method includes the following steps:

[0012] Step S1: Set the input data X, the number of model instances S, and the number of sampling times M;

[0013] Step S2: By improving the algorithm AGS, sampling weights and information theory principles are used to select effective data, and then a subset of data is selected from the effective data to generate M model hypotheses;

[0014] Step S3: Calculate the discrimination distance matrix A using the generated M model assumptions;

[0015] Step S4: Calculate the sparse distance matrix using information theory and A.

[0016] Step S5: In Then, use parameter S to perform spectral clustering to obtain the class label of X.

[0017] Step S3 specifically includes the following steps:

[0018] Step S31: For each model, assume θ i Calculate the input data X and θ i residual r i ;

[0019] Step S32: Estimate r using the scaling estimator MSSE i The interior point scale σ;

[0020] Step S33: The elements of the model matrix H are calculated as follows:

[0021]

[0022] Step S34: Calculate the discrimination distance matrix A←HH T .

[0023] The calculation of the sparse distance matrix in step S4 specifically includes the following steps:

[0024] Step S41: For the i-th row element A of the sparse distance matrix A i =[A i，1 A i，2 A i，N ], calculate the distance between the largest element and the j-th element.

[0025] Step S42: The probability of the j-th element is calculated as follows:

[0026] Step S43: The threshold for the i-th row is calculated as follows

[0027] Step S44: Set the values ​​of elements less than E to 0; otherwise, their values ​​remain unchanged. The formula is as follows:

[0028]

[0029] Step S45: After performing the above four steps on each row of the distance matrix A, the resulting matrix A is... * It is not symmetric, but the required distance matrix is ​​symmetric, through A symmetric matrix is ​​obtained.

[0030] The spectral clustering performed in step S5 specifically includes the following steps:

[0031] Step S51: Calculate the degree matrix

[0032] Step S52: Calculate the Laplacian matrix

[0033] Step S53: Calculate the eigenvalues ​​of L, sort the eigenvalues ​​from smallest to largest, take the first S eigenvalues, and calculate the eigenvectors u1, u2, ..., u of the first S eigenvalues. S ;

[0034] Step S54: Combine the above S eigenvectors into a matrix U = {u1, u2, ..., u...} S}, U∈R n*S ;

[0035] Step S55: Let y i ∈R S Let be the i-th row vector of U, where i = 1, 2, ..., n;

[0036] Step S56: y i Normalization makes |y i |=1;

[0037] Step S57: Use the k-means algorithm to generate new sample points Y = {y1, y2, ..., y...} S Clustered into clusters C1, C2, ..., C S The steps are as follows: randomly select S objects as initial cluster centers, and then perform the following process.

[0038] Process (1): Calculate the distance between each object and each cluster center, and assign each object to the cluster corresponding to the nearest cluster center;

[0039] In process (2), each cluster center is updated to the average value of all points in that cluster;

[0040] Repeat steps (1) and (2) until no objects are reassigned to different cluster centers.

[0041] When the fitting method is used to segment two-dimensional moving objects in a scene graph, the distance matrix is ​​generated using scene graph data containing multiple two-dimensional moving objects. The fitting method uses the class label of X in step S5 to segment the data in the image that belong to two-dimensional moving objects into points belonging to different moving objects.

[0042] The fitting method is used in the fields of computer vision or artificial intelligence.

[0043] The fitting method is used for robust models, which are used for feature-based image registration, pose estimation, multi-target tracking, PPS signal estimation, FM signal estimation, or 3D motion segmentation.

[0044] The method described in this invention effectively combines the advantages of residual sorting and sparsity constraints, and can efficiently generate a more accurate distance matrix for data containing multiple model instances and a high proportion of outliers.

[0045] This invention can be used as a sampling method in various fields of computer vision and artificial intelligence, such as feature-based image registration, pose estimation, multi-object tracking, PPS and FM signal estimation, and 3D motion segmentation. Attached Figure Description

[0046] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0047] Appendix Figure 1 This is a flowchart illustrating the present invention;

[0048] Appendix Figure 2 This is a schematic diagram of two-dimensional moving object segmentation using the method of this embodiment. Detailed Implementation

[0049] As shown in the figure, a basic matrix fitting method based on residual sorting and sparsity constraints is used to generate an effective distance matrix for a dataset containing multiple model instances and a high proportion of outliers. The method includes the following steps.

[0050] Step S1: Set the input data X, the number of model instances S, and the number of sampling times M;

[0051] Step S2: By improving the algorithm AGS, sampling weights and information theory principles are used to select effective data, and then a subset of data is selected from the effective data to generate M model hypotheses;

[0052] Step S3: Calculate the discrimination distance matrix A using the generated M model assumptions;

[0053] Step S4: Calculate the sparse distance matrix using information theory and A.

[0054] Step S5: In Then, use parameter S to perform spectral clustering to obtain the class label of X.

[0055] Step S3 specifically includes the following steps:

[0056] Step S31: For each model, assume θ i Calculate the input data X and θ i residual r i ;

[0057] Step S32: Estimate r using the scaling estimator MSSE i The interior point scale σ;

[0058] Step S33: The elements of the model matrix H are calculated as follows:

[0059]

[0060] Step S34: Calculate the discrimination distance matrix A←HH T .

[0061] The calculation of the sparse distance matrix in step S4 specifically includes the following steps:

[0062] Step S41: For the i-th row element A of the sparse distance matrix A i =[A i，1 A i，2 A i，N ], calculate the distance between the largest element and the j-th element.

[0063] Step S42: The probability of the j-th element is calculated as follows:

[0064] Step S43: The threshold for the i-th row is calculated as follows

[0065] Step S44: Set the values ​​of elements less than E to 0; otherwise, their values ​​remain unchanged. The formula is as follows:

[0066]

[0067] Step S45: After performing the above four steps on each row of the distance matrix A, the resulting matrix A is... * It is not symmetric, but the required distance matrix is ​​symmetric, through A symmetric matrix is ​​obtained.

[0068] The spectral clustering performed in step S5 specifically includes the following steps:

[0069] Step S51: Calculate the degree matrix

[0070] Step S52: Calculate the Laplacian matrix

[0071] Step S53: Calculate the eigenvalues ​​of L, sort the eigenvalues ​​from smallest to largest, take the first S eigenvalues, and calculate the eigenvectors u1, u2, ..., u of the first S eigenvalues. S ;

[0072] Step S54: Combine the above S eigenvectors into a matrix U = {u1, u2, ..., u...} S}, U∈R n+s ;

[0073] Step S55: Let y i ∈R s Let be the i-th row vector of U, where i = 1, 2, ..., n;

[0074] Step S56: y i Normalization makes |y i |=1;

[0075] Step S57: Use the k-means algorithm to generate new sample points Y = {y1, y2, ..., y...} S Clustered into clusters C1, C2, ..., C S The steps are as follows: randomly select S objects as initial cluster centers, and then perform the following process.

[0076] Process (1): Calculate the distance between each object and each cluster center, and assign each object to the cluster corresponding to the nearest cluster center;

[0077] In process (2), each cluster center is updated to the average value of all points in that cluster;

[0078] Repeat steps (1) and (2) until no objects are reassigned to different cluster centers.

[0079] like Figure 2 As shown, when the fitting method is used to segment two-dimensional moving objects in a scene graph, the distance matrix is ​​generated using scene graph data containing multiple two-dimensional moving objects. The fitting method uses the class label of X in step S5 to segment the data in the image that belong to two-dimensional moving objects into points belonging to different moving objects.

[0080] like Figure 2 As shown, in this embodiment, Figure 2 The six scene images in the example are used as input image data for the method of this embodiment. After the steps of this embodiment, the output class labels divide the data in the image into points belonging to different moving objects, and the points of different objects are identified by different shapes.

[0081] The fitting method is used in the fields of computer vision or artificial intelligence.

[0082] The fitting method is used for robust models, which are used for feature-based image registration, pose estimation, multi-target tracking, PPS signal estimation, FM signal estimation, or 3D motion segmentation.

Claims

1. A fundamental matrix fitting method based on residual sorting and sparsity constraints, characterized in that: The fitting method generates an effective distance matrix for a dataset containing multiple model instances and a high proportion of outliers, specifically including the following steps: Step S1: Set input data The number of model instances is S, and the number of samplings is M; Step S2: By improving the algorithm AGS, sampling weights and information theory principles are used to select effective data, and then a subset of data is selected from the effective data to generate M model hypotheses; Step S3: Calculate the discrimination distance matrix using the generated M model hypotheses. ; Step S4: Using information theory and Calculate the sparse distance matrix ; Step S5: In Use parameter S to perform spectral clustering to obtain Class label; Step S3 specifically includes the following steps: Step S31: For each model hypothesis Calculate the input data and residual ; Step S32: Estimate using the scaling estimator MSSE Interior point scale ; Step S33: The elements of the model matrix H are calculated as follows: Formula (1) Step S34: Calculate the discrimination distance matrix ; The calculation of the sparse distance matrix in step S4 specifically includes the following steps: Step S41: For the sparse distance matrix The i-th row element Calculate the distance between the largest element and the j-th element. ; Step S42: The probability of the j-th element is calculated as follows: ; Step S43: The threshold for the i-th row is calculated as follows ; Step S44: For values ​​less than... The element is set to 0, otherwise its value remains unchanged. The formula is as follows: Formula (II); Step S45: For the distance matrix After performing the above four steps on each row, the resulting matrix It is not symmetric, but the required distance matrix is ​​symmetric, through Obtain a symmetric matrix; The spectral clustering performed in step S5 specifically includes the following steps: Step S51: Calculate the degree matrix ; Step S52: Calculate the Laplacian matrix ; Step S53: Calculation The eigenvalues ​​are sorted in ascending order, and the first S eigenvalues ​​are selected. The eigenvectors of the first S eigenvalues ​​are then calculated. ; Step S54: Form a matrix from the above S eigenvectors. ; Step S55: Let yes The i-th row vector, where i = 1, 2, ..., n; Step S56: ... Unitization makes ; Step S57: Use the k-means algorithm to process the new sample points Clustering The steps are as follows: randomly select S objects as initial cluster centers, and then perform the following process. Process (1): Calculate the distance between each object and each cluster center, and assign each object to the cluster corresponding to the nearest cluster center; In process (2), each cluster center is updated to the average of all points in that cluster; Repeat steps (1) and (2) until no objects are reassigned to different cluster centers; The fitting method is used in the fields of computer vision or artificial intelligence; when used to segment two-dimensional moving objects in a scene graph, the distance matrix is ​​generated using scene graph data containing multiple two-dimensional moving objects, and the fitting method is based on step S5. The class labels are used to segment the data of two-dimensional moving objects in the image into points belonging to different moving objects.

2. The fundamental matrix fitting method based on residual sorting and sparsity constraints according to claim 1, characterized in that: The fitting method is used for robust models, which are used for feature-based image registration, pose estimation, multi-target tracking, PPS signal estimation, FM signal estimation, or 3D motion segmentation.

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