Underwater hyperspectral image clustering method based on multi-scale anchor image

Abstract

The invention discloses an underwater hyperspectral image clustering method based on a multi-scale anchor image, and belongs to the technical field of underwater image processing. The method mainly comprises the following steps: carrying out superpixel segmentation on an underwater hyperspectral image; performing noise removal processing on the segmented hyperspectral image; learning a multi-scale anchor image of the denoised hyperspectral image; matrix decomposition is carried out on the multi-scale anchor images, and soft labels of super-pixel points are obtained; stacking the soft label matrixes into a tensor, and introducing a tensor Schatten-p norm to obtain a high-dimensional space structure of the multi-scale anchor map; constructing an optimization objective function; updating the target function variable by using an iterative updating strategy; and carrying out adaptive fusion on the learned soft label matrix. According to the method, pixel point soft labels are obtained mainly through multi-scale anchor image decomposition, label matrixes are stacked into tensors to explore a high-dimensional space structure of data, finally, self-adaptive weighted summation is conducted on the soft labels of the multi-scale anchor images to obtain a label result used for clustering analysis, and the clustering precision is remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of underwater hyperspectral image processing, and in particular to an underwater hyperspectral image clustering method based on a multi-scale anchor graph. Background Art

[0002] Hyperspectral imaging is an important remote sensing technology that captures the electromagnetic spectrum from visible light to the near-infrared band. In a hyperspectral image, each pixel can be viewed as a high-dimensional vector, where the pixel value corresponds to the spectral reflectance at a specific wavelength.

[0003] Hyperspectral image clustering is an unsupervised learning method based on hyperspectral data. It analyzes the spectral characteristics of pixels in an image and groups pixels with similar characteristics into distinct categories. Because hyperspectral images contain rich spectral information, clustering algorithms can effectively identify object type, material composition, or tissue characteristics. It is widely used in remote sensing classification, target detection, and medical image analysis, enabling rapid segmentation and understanding of complex scenes.

[0004] Clustering underwater hyperspectral images can effectively extract the spectral characteristics of underwater targets and distinguish different substances or biological species, such as corals, seaweeds, and sediments. Therefore, how to improve the clustering accuracy of underwater hyperspectral images is a major problem that we urgently need to solve. Summary of the Invention

[0005] In light of the shortcomings of existing technologies, this paper provides a method for underwater hyperspectral image clustering based on multi-scale anchor maps. This method primarily utilizes multi-scale anchor map decomposition to obtain soft labels for pixel points. This label matrix is ​​then stacked into a tensor to explore the high-dimensional spatial structure of the data. Finally, an adaptive weighted summation of the soft labels from the multi-scale anchor map is performed to obtain labeling results for cluster analysis, significantly improving clustering accuracy.

[0006] The technical means adopted in the present invention are as follows:

[0007] A multi-scale anchor chart-based underwater hyperspectral image clustering method comprises the following steps:

[0008] Step 1: Get the given hyperspectral data X∈R W×H×B , where W×H represents the number of pixels in the underwater hyperspectral image, and B is the number of bands contained in the underwater hyperspectral image;

[0009] Step 2: Use the entropy rate superpixel segmentation method to segment the underwater hyperspectral image to obtain a number of superpixel points, each of which contains a number of pixel points;

[0010] Step 3: Denoise the hyperspectral image with superpixels as the smallest unit, and maintain the sparsity of the noise;

[0011] Step 4: Learn the multi-scale anchor map of the denoised hyperspectral image to extract spectral information at different levels;

[0012] Step 5: Perform matrix decomposition on anchor images of multiple scales to obtain soft labels of superpixel points;

[0013] Step 6: Stack the soft label matrix into a tensor and introduce the tensor Schatten-p norm. While maintaining the low rank of the soft label, the complementary information of anchor maps at different scales is utilized to obtain the high-dimensional spatial structure of the multi-scale anchor map.

[0014] Step 7: Combine the multi-scale anchor map, soft labels, and tensor Schatten-p norm into a unified framework, and introduce corresponding auxiliary variables to construct the optimization objective function;

[0015] Step 8: Use the iterative update strategy to update a certain variable while keeping other variables fixed;

[0016] Step 9: Adaptively fuse the learned soft label matrix to obtain the soft label of the superpixel point, and take the index corresponding to the maximum value of the soft label as the final cluster category.

[0017] Furthermore, the entropy rate superpixel segmentation method is used to segment the underwater hyperspectral image to obtain several superpixel points, including:

[0018] The underwater hyperspectral image is subjected to principal component analysis and dimensionality reduction processing. The band dimension is reduced to 3 dimensions, and then entropy rate superpixel segmentation is performed to assign each pixel point to its corresponding superpixel point.

[0019] Furthermore, the entropy rate superpixel segmentation adopts the following formula:

[0020]

[0021] in represents the i-th superpixel region with the same segmentation label, and the constraint Indicates that any two generated superpixel regions are non-overlapping, I f represents the original underwater hyperspectral image composed of multiple segmented superpixel regions, and M represents the total number of segmented superpixel points.

[0022] Furthermore, a multi-scale anchor map of the denoised hyperspectral image is learned according to the following formula to extract spectral information at different levels:

[0023]

[0024] where W∈R R×B Represents the projection matrix of underwater hyperspectral image, X∈RB×N Represents the original underwater hyperspectral image, Y∈R B×N represents the denoised underwater hyperspectral image, represents the v-th anchor matrix, represents the anchor graph of the vth scale, α (v) Represents the weight of the v-th scale anchor graph, E∈R B×N represents the noise matrix in the underwater hyperspectral image, λ1, λ2 and r represent the regularization parameters.

[0025] Furthermore, the soft label matrix is ​​stacked into a tensor, and the tensor Schatten-p norm is introduced, using the following formula:

[0026]

[0027] in represents the anchor graph of the vth scale, represents the basis matrix of the v-th scale anchor graph, F (v) ∈R c×N Represents the label matrix corresponding to the anchor graph of the vth scale, represents a tensor, α (v) represents the weight of the v-th scale anchor graph, λ3 and r represent regularization parameters.

[0028] Furthermore, the optimization objective function is:

[0029]

[0030] where Q and is the auxiliary variable introduced, Y1, and is the Lagrange multiplier and μ is the penalty parameter.

[0031] Compared with the prior art, the present invention has the following advantages:

[0032] The present invention discloses a method for clustering underwater hyperspectral images by obtaining soft labels of pixel points through multi-scale anchor graph decomposition. First, the underwater hyperspectral image is segmented into superpixels to obtain a plurality of superpixels containing multiple pixels. Then, the underwater hyperspectral image with superpixels as the smallest unit is subjected to noise removal. Then, a multi-scale anchor graph of the processed underwater hyperspectral image is calculated to extract information at different levels while reducing complexity. Then, the multi-scale anchor graph is subjected to matrix decomposition to obtain soft labels of superpixels corresponding to different anchor graphs. The label matrix is ​​stacked into a tensor to explore the high-dimensional spatial structure of the data. Finally, the soft labels of the multi-scale anchor graph are adaptively weighted summed to obtain the final result. The present invention calculates the multi-scale anchor graph of the processed underwater hyperspectral data to obtain more comprehensive spectral information, and performs matrix decomposition on it to directly obtain soft labels of superpixels, avoiding the time consumption and information loss caused by post-processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative labor.

[0034] Figure 1 This is a flow chart of an underwater hyperspectral image clustering method based on a multi-scale anchor graph in an embodiment of the present invention.

[0035] Figure 2 This is a diagram of an underwater hyperspectral image clustering execution architecture based on a multi-scale anchor map in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] In order to enable those skilled in the art to better understand the solutions of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the embodiments described are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts should fall within the scope of protection of the present invention.

[0037] like Figure 1 As shown, the present invention provides an underwater hyperspectral image clustering method based on a multi-scale anchor graph, which mainly includes the following steps:

[0038] Step 1: Given hyperspectral data X∈R W×H×B , where W×H represents the number of pixels in the underwater hyperspectral image, and B is the number of included bands.

[0039] Step 2: Use the entropy rate superpixel segmentation method to segment the underwater hyperspectral image into several superpixels. Each superpixel contains several pixels and is regarded as a region with similar characteristics.

[0040] Entropy rate superpixel segmentation uses the following formula:

[0041]

[0042] in represents the i-th superpixel region with the same segmentation label, and the constraint Indicates that any two generated superpixel regions are non-overlapping, I f represents the original underwater hyperspectral image composed of multiple segmented superpixel regions, and M represents the total number of segmented superpixel points.

[0043] Computation I f The corresponding superpixel point is as follows:

[0044]

[0045] where x i represents the calculated i-th superpixel point, represents the kth original pixel in the i-th similarity region. This formula fully explores the spectral data of superpixels composed of pixels with similar characteristics.

[0046] Step 3: Denoise the hyperspectral image with superpixels as the smallest unit, and maintain the sparsity of the noise;

[0047] The denoising operation of underwater hyperspectral images can be obtained by the following formula:

[0048]

[0049] stX=Y+E

[0050] where X∈R B×N Represents the original underwater hyperspectral image, Y∈R B×N represents the denoised underwater hyperspectral image, E∈R B×N represents the noise matrix in the underwater hyperspectral image, and λ2 represents the regularization parameter.

[0051] Step 4: Learn multi-scale anchor maps for denoised data To extract spectral information at different levels;

[0052] The learning of multi-scale anchor maps is as follows:

[0053]

[0054] where W∈R R×B represents the projection matrix, represents the v-th anchor matrix, represents the anchor graph of the vth scale, α (v) represents the weight of the v-th scale anchor graph, λ1 and r represent regularization parameters.

[0055] Step 5: Perform matrix decomposition on anchor images of various scales to directly obtain soft labels of superpixels To reduce the time complexity of the algorithm.

[0056] The soft label of the superpixel can be obtained by the following formula:

[0057]

[0058] in represents the basis matrix of the v-th scale anchor graph obtained based on matrix decomposition, F (v) ∈R c×N Represents the label matrix corresponding to the anchor image of the vth scale.

[0059] Step 6: Introduce the tensor Schatten-p norm, which utilizes the complementary information of anchor images of different scales while maintaining the low rank of soft labels.

[0060] The learning of the structure between soft labels is as follows:

[0061]

[0062] Where λ3 and p represent regularization parameters, represents a tensor, F (1) ,F (2) ,...,F (V) represents the label matrix corresponding to the anchor graphs of different scales, and Φ represents the stacking function. And Where V represents the number of soft label matrices learned based on anchor maps of different scales, c represents the number of clusters, and N represents the number of superpixels that need to be clustered. express The jth singular value of express The i-th vertical slice of .

[0063] Step 7: Combine the above steps into a unified framework and introduce corresponding auxiliary variables for optimization;

[0064] The overall formula for step 7.1 is as follows:

[0065]

[0066] The optimization formula after adding auxiliary variables in step 7.2 is as follows:

[0067]

[0068]

[0069] in and is the auxiliary variable introduced, Y1, and is the Lagrange multiplier, μ is the parameter.

[0070] Step 8: Use the iterative update strategy to update a certain variable while keeping other variables fixed.

[0071] Step 8.1 Update W and fix other variables to obtain:

[0072]

[0073] The above formula is equivalent to:

[0074]

[0075] in

[0076] The solution of W is (YY T ) -1 The eigenvectors corresponding to the R smallest eigenvalues ​​of G.

[0077] Step 8.2 Update Y and fix other variables to obtain:

[0078]

[0079] Taking the derivative of the above formula with respect to Y and setting it to 0, we can get:

[0080]

[0081] Step 8.3 Update A (v) , fixing other variables, we can get:

[0082]

[0083] For the above formula about A (v) Taking the derivative and setting it to 0, we get:

[0084] A (v) =(Y(Z (v) ) T )(Z (v) (Z (v) )T ) -1

[0085] Step 8.4 Update Z (v) , fixing other variables, we can get:

[0086]

[0087] For the above formula about Z (v) Taking the derivative and setting it to 0, we get:

[0088] Z (v) =((λ1+1)I+(A (v) ) T A (v) ) -1 (M (v) (F (v) ) T +(A (v) ) T Y)

[0089] Step 8.5 Update E and fix other variables to obtain:

[0090]

[0091] The above formula has the following closed-form solution:

[0092]

[0093] where θ is the contraction operator.

[0094] Step 8.6 Update M (v) , fixing other variables, we can get:

[0095]

[0096] For the above formula about M (v) Taking the derivative and setting it to 0, we get:

[0097] M (v) =Z (v) F (v)

[0098] Step 8.7 Update Fixing other variables yields:

[0099]

[0100] The above formula has the following optimal solution:

[0101]

[0102] in is a diagonal tensor whose diagonal elements can be obtained based on the GST algorithm. Step 8.8 Update K (v) , fixing other variables, we can get:

[0103]

[0104] sqFt (v) ≥0

[0105] For the above formula about K (v) Taking the derivative and setting it to 0, we get:

[0106]

[0107] Step 8.9 Update F (v) , fixing other variables, we can get:

[0108]

[0109] The above formula is equivalent to:

[0110]

[0111] Among them G (v) =2(α (v) ) r (Z (v) ) T M (v) +μQ (v) -Y2 (v) +μK (v) -Y3 (v) , F (v) The solution to G (v) Perform a truncated singular value decomposition to find .

[0112] Step 8.10 Update α (v) , fixing other variables, we can get:

[0113]

[0114] For the above formula about α (v) Taking the derivative and setting it to 0, we get:

[0115]

[0116] in

[0117] Step 8.11 Update Y1, and μ, and fixing other variables, we can get:

[0118] Y1=Y1+μ(XYE)

[0119]

[0120] μ=min(ρμ,μ0)

[0121] Step 9: Adaptively fuse the learned soft label matrix to obtain the soft label of the superpixel point, and take the index corresponding to the maximum value of the soft label as the final cluster category.

[0122] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-scale anchor graph-based underwater hyperspectral image clustering method, characterized in that: The following steps are involved: Step 1: Get the given hyperspectral data X∈R W×H×B , where W×H represents the number of pixels in the underwater hyperspectral image, and B is the number of bands contained in the underwater hyperspectral image; Step 2: Use the entropy rate superpixel segmentation method to segment the underwater hyperspectral image to obtain a number of superpixel points, each of which contains a number of pixel points; Step 3: Denoise the hyperspectral image with superpixels as the smallest unit, and maintain the sparsity of the noise; Step 4: Learn the multi-scale anchor map of the denoised hyperspectral image to extract spectral information at different levels; Step 5: Perform matrix decomposition on anchor images of multiple scales to obtain soft labels of superpixel points; Step 6: Stack the soft label matrix into a tensor and introduce the tensor Schatten-p norm. While maintaining the low rank of the soft label, the complementary information of anchor maps at different scales is utilized to obtain the high-dimensional spatial structure of the multi-scale anchor map. Step 7: Combine the multi-scale anchor map, soft labels, and tensor Schatten-p norm into a unified framework, and introduce corresponding auxiliary variables to construct the optimization objective function; Step 8: Use the iterative update strategy to update a certain variable while keeping other variables fixed; Step 9: Adaptively fuse the learned soft label matrix to obtain the soft label of the superpixel point, and take the index corresponding to the maximum value of the soft label as the final cluster category.

2. The underwater hyperspectral image clustering method based on multi-scale anchor chart according to claim 1, characterized in that: The entropy rate superpixel segmentation method is used to segment the underwater hyperspectral image and obtain several superpixel points, including: The underwater hyperspectral image is subjected to principal component analysis and dimensionality reduction processing. The band dimension is reduced to 3 dimensions, and then entropy rate superpixel segmentation is performed to assign each pixel point to its corresponding superpixel point.

3. The underwater hyperspectral image clustering method based on multi-scale anchor chart according to claim 2, characterized in that: The entropy rate superpixel segmentation adopts the following formula: in represents the i-th superpixel region with the same segmentation label, and the constraint Indicates that any two generated superpixel regions are non-overlapping, I f represents the original underwater hyperspectral image composed of multiple segmented superpixel regions, and M represents the total number of segmented superpixel points.

4. The underwater hyperspectral image clustering method based on multi-scale anchor chart according to claim 3, characterized in that: The multi-scale anchor map of the denoised hyperspectral image is learned according to the following formula to extract spectral information at different levels: where W∈R R×B Represents the projection matrix of underwater hyperspectral image, X∈R B×N Represents the original underwater hyperspectral image, Y∈R B×N represents the denoised underwater hyperspectral image, represents the v-th anchor matrix, represents the anchor graph of the vth scale, α (v) Represents the weight of the v-th scale anchor graph, E∈R B×N represents the noise matrix in the underwater hyperspectral image, λ1, λ2 and r represent the regularization parameters.

5. The underwater hyperspectral image clustering method based on multi-scale anchor chart according to claim 4, characterized in that: The soft label matrix is ​​stacked into a tensor, and the tensor Schatten-p norm is introduced using the following formula: in represents the anchor graph of the vth scale, represents the basis matrix of the v-th scale anchor graph, F (v) ∈R c×N Represents the label matrix corresponding to the anchor graph of the vth scale, represents a tensor, α (v) represents the weight of the v-th scale anchor graph, λ3 and r represent regularization parameters.

6. The underwater hyperspectral image clustering method based on multi-scale anchor chart according to claim 5, characterized in that: The optimization objective function is: in and is an auxiliary variable introduced, and is the Lagrange multiplier and μ is the penalty parameter.

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