A Mangrove Extraction Method Based on Orthogonal Matched Filtering-Weighted Least Squares

Abstract

This invention discloses a mangrove extraction method based on orthogonal matched filtering and weighted least squares, relating to the fields of remote sensing and image processing. This method, through preprocessing and band extension, combines whitened orthogonal subspace projection with a whitened matched filter method to effectively enhance mangrove feature information. Subsequently, weighted least squares filtering is introduced to further enhance the edge information of the mangrove image. Finally, Otsu's method is used to adaptively threshold segment the remote sensing image, thereby achieving target extraction of the mangrove region. It possesses advantages such as low cost, high accuracy, and short processing time. It solves the problems of high labor costs and low efficiency in existing technologies, insufficient representativeness and coverage of neural network methods, inability to effectively identify and extract mangroves in various complex backgrounds, and low adaptability and accuracy.

Description

Technical Field

[0001] This invention belongs to the field of remote sensing and image processing technology, specifically relating to a mangrove extraction method based on orthogonal matched filtering-weighted least squares. Background Technology

[0002] As an important marine-terrestrial interactive ecosystem, the health and stability of mangrove ecosystems are crucial for maintaining marine biodiversity and marine ecological balance. Therefore, to achieve sustainable development of mangroves, it is necessary to strengthen management and supervision, adopt scientific environmental protection measures, ensure the healthy interaction of mangroves, protect the marine ecological environment, and achieve sustainable use of resources.

[0003] Currently, traditional manual surveys and monitoring are too slow, requiring multiple on-site measurements and consuming significant manpower and resources, gradually failing to meet the growing monitoring demands. In recent years, with the development of remote sensing technology and the increasing precision of optical sensors, remote sensing, with its advantages of large scale, short cycle time, real-time monitoring, and low cost, has gradually become one of the most important monitoring methods. This is particularly advantageous for the ecosystems of nature reserves like mangroves, where remote sensing monitoring can quickly obtain spatial distribution information of mangroves by utilizing the continuity of its sensor system and image acquisition capabilities. The Gaofen series satellites play a positive and important role in improving my country's natural resource asset property rights system and land use management system, delineating ecological protection red lines, implementing a system of paid use of resources and ecological compensation, and reforming the ecological and environmental protection management system. The Gaofen-6 (GF-6) remote sensing satellite is a typical example, characterized by high resolution, wide coverage, high-quality imaging, high-efficiency imaging, and high domestic production rate. Remote sensing image target detection, as an important branch of remote sensing data processing, has seen the development of many target detection methods, such as spectral angle mapping, orthogonal subspace projection, matched filters, and constrained energy minimization.

[0004] While manual visual interpretation can yield accurate results, it is costly and inefficient, and ineffective when dealing with large-scale data. Although neural networks have seen rapid development recently, they often require large datasets for thorough training to function effectively in practical applications. While some training datasets exist, these are insufficient to meet the growing demands of remote sensing applications. Existing datasets are often limited to specific regions or crop types, lacking sufficient representativeness and coverage. Furthermore, the quality of the dataset and the accuracy of the annotations affect the performance and generalization ability of neural network models. When dealing with large-area data, runtime constraints severely limit the need for rapid observation. Currently, research on remote sensing image data processing focuses on data augmentation and semi-supervised learning. Data augmentation techniques improve the model's data utilization and generalization ability by transforming and expanding existing data. Semi-supervised learning utilizes a small amount of labeled data and a large amount of unlabeled data, improving the model's generalization ability and adaptability through self-supervised or semi-supervised learning methods. However, this method still suffers from problems such as the inability to effectively identify and extract mangroves in various complex backgrounds, and low adaptability and accuracy.

[0005] Based on this, the present invention proposes a mangrove extraction method based on orthogonal matched filtering and weighted least squares, aiming to solve the problems existing in the above-mentioned prior art and provide more reliable technical support for mangrove resource monitoring and protection. Summary of the Invention

[0006] In view of this, the main objective of this invention is to provide a mangrove extraction method based on orthogonal matched filtering and weighted least squares, in order to solve the problems of high labor costs and low efficiency, insufficient representativeness and coverage of neural network methods, inability to effectively identify and extract mangroves in various complex backgrounds, and low adaptability and accuracy in the above-mentioned existing technologies; it effectively improves the extraction performance in complex mangrove backgrounds and has the advantages of high efficiency, simplicity and reliability, and high accuracy.

[0007] To achieve the above objectives, the technical solution of the present invention is implemented as follows:

[0008] A mangrove forest extraction method based on orthogonal matched filtering-weighted least squares includes:

[0009] Step 1: Acquire the original multispectral remote sensing images and preprocess and fuse them;

[0010] Step 2: Perform land-sea separation processing on the multispectral fused remote sensing image;

[0011] Step 3: After separating the land and sea in the multispectral fused remote sensing image, the average spectrum of the prior information is obtained from the spectral library based on the spectral information of the mangroves collected multiple times.

[0012] Step 4: After obtaining prior information, feature indices are constructed through band expansion, and mangroves are further distinguished through feature indices;

[0013] Step 5: Perform two-dimensionalization and normalization on the remote sensing image data obtained in Step 4;

[0014] Step 6: Based on the orthogonal subspace projection and matched filter method, add whitening and regularization terms to the remote sensing image data processed in Step 5;

[0015] Step 7: By combining the orthogonal subspace projection and matched filter method optimized in Step 6, a new orthogonal matched filtering method is obtained;

[0016] Step 8: Introduce the weighted least squares method into the new orthogonal matched filtering method obtained in step 7 to obtain a mangrove extraction method based on orthogonal matched filtering-weighted least squares. Finally, use the Otsu method for threshold segmentation to realize the identification and extraction of mangroves.

[0017] In a preferred embodiment of the present invention, the process of preprocessing and fusing the remote sensing image in step 1 includes:

[0018] Step 1.1: Select the area to be acquired and obtain the original multispectral remote sensing image of the area, and preprocess the image;

[0019] The preprocessing procedure for raw multispectral remote sensing images includes radiometric calibration, atmospheric correction, and orthorectification.

[0020] Step 1.2: After preprocessing the original multispectral remote sensing image, the multispectral image and the panchromatic image are fused to obtain a high-resolution multispectral fused remote sensing image.

[0021] The image fusion method used is the Gram-Schmidt method.

[0022] In a preferred embodiment of the present invention, when performing land-sea separation processing on the multispectral fused remote sensing image in step 2, the vector elements of the multispectral fused remote sensing image are first edited using embedded GIS, and then masking is performed.

[0023] In a preferred embodiment of the present invention, the characteristic indices in step 4 include the normalized vegetation index, the enhanced vegetation index, the normalized differential water body index, and the total suspended solids concentration index.

[0024] In a preferred embodiment of the present invention, step 5, the process of performing two-dimensionalization and normalization on the remote sensing image data, includes:

[0025] Step 5.1: Convert the 3D multispectral image into a 2D matrix and map the data to between 0 and 1, removing the dimensions and units of the data from different dimensions;

[0026] Step 5.2: Next, perform average normalization on the data to center the data at 0, and then standardize the data; the specific process is as follows:

[0027] Given the covariance matrix:

[0028]

[0029] Since the data has been normalized to the mean, Therefore, equation (1) is transformed into:

[0030]

[0031] Then, eigenvalue decomposition is performed on the covariance matrix C to calculate the eigenvalues ​​and eigenvectors, resulting in:

[0032] C = UAU T (3)

[0033] In equation (3), U is the eigenvector, Λ is the diagonal matrix, and the elements on the diagonal are the eigenvalues.

[0034] In a preferred embodiment of the present invention, the solution process of the orthogonal subspace projection method in step 5 includes:

[0035] Step 6.1.1: First, let X be an L×1 dimensional pixel spectral vector, K represent the dimension of the endmember spectral matrix, and α i The abundance of the corresponding endmember is represented by the expression:

[0036]

[0037] The OSP model consists of the target signal d and the background endmember U, therefore we get:

[0038]

[0039] In equation (5), Let be the abundance vector of the target signal. is the abundance vector of background endmembers, and n is the noise or model error;

[0040] Step 6.1.2: Introduce an orthogonal subspace projector, defined as:

[0041]

[0042] In equation (6), ⊥ is the orthogonal complement space, I is the K×K dimensional identity matrix, (U T U) -1 U T Let U be the pseudo-inverse of matrix U. T This represents the transpose of matrix U;

[0043] The constructed filter detector is as follows:

[0044]

[0045] In a preferred embodiment of the present invention, the solution process of the matched filter method in step 5 includes:

[0046] Step 6.2.1: Suppose the image to be identified has B bands, and the vector form of each pixel is:

[0047] x s = [x1, x2, x3, ..., x B ] T (s=1,2,3,…,S) (8)

[0048] In equation (8), S = LEN × WID, where LEN is the length of the image size and WID is the width of the image size. Each band of the sensor will acquire a grayscale image G of size S. b :

[0049] G b (len,wid)(b=1,2,3,…,B;len=1,2,3,…,LEN;wid=1,2,3,…,WID)(9)

[0050] Step 6.2.2: Rearrange the 3D image data as follows:

[0051] X = [x1, x2, x3, ..., x S (10)

[0052] The expression is as follows:

[0053] X(b,s)(b=1,2,3,…,B; s=1,2,3,…,S) (11)

[0054] The relationship between equation (9) and equation (11) is as follows:

[0055] G b (len,wid)=X(b,(len-1)WID+wid) (12)

[0056] Step 6.2.3: Based on prior information, reduce the matched filter (MF) algorithm for single-target detection to a quadratic programming problem:

[0057]

[0058] In equation (13), μ1 is the mean vector of the target pixel, μ0 is the mean vector of the background pixel, and W is a linear filter;

[0059] We introduce the Lagrange multiplier method to solve for the unknown vector W:

[0060]

[0061] Background covariance matrix and background mean vector Based on existing data, it is estimated that:

[0062]

[0063] The linear detector takes the form of:

[0064]

[0065] The target mean vector is obtained by averaging existing spectral libraries or label information:

[0066]

[0067] Step 6.2.4: Combining the data from equations (14) to (18), perform Mahalanobis distance calculation between the target and the background to obtain:

[0068]

[0069] As a preferred embodiment of the present invention, step 5, which involves adding whitening and regularization terms to the remote sensing image data, includes:

[0070] Step 6.3.1: By combining the features x of each dimension rot,i Divide by the square root of its corresponding eigenvalue Scaling the data yields a PCA-whitened data matrix:

[0071]

[0072] Adding a regularization term constant ε to the data matrix yields the final PCA whitening matrix:

[0073]

[0074] Step 6.3.2: Perform whitening weighted operations on equations (5)-(7) and (21) to obtain:

[0075]

[0076] Therefore, the detector is redefined as:

[0077]

[0078] Step 6.3.3: Project the orthogonal subspace in equation (23) Constructing a sparse matrix yields the whitened sample space as follows:

[0079]

[0080] Therefore, MF is rewritten as:

[0081]

[0082] In equation (25), It is a constant.

[0083] As a preferred embodiment of the present invention, step 7, which combines the orthogonal subspace projection and matched filter method optimized in step 6 to obtain the orthogonal matched filter method, includes:

[0084] Step 7.1: First, the projection vector W is found using a new measurement method. In the whitening space, W is found by minimizing it, and a new output is obtained:

[0085]

[0086] Step 7.2: Next, change d in equation (22) white As the target vector in the matched filter A new orthogonal matched filter optimization model is formed, and the constrained minimization problem becomes:

[0087]

[0088] Step 7.3: Finally, the new orthogonal matched filter optimization model is expanded and simplified as follows:

[0089]

[0090] In equation (28), Σ OMF Let represent the autocovariance matrix of the weighted whitened samples. In the whitening space, the covariance matrix is ​​the identity matrix. Solving the new orthogonal matched filter optimization model yields:

[0091]

[0092] Therefore, the final output of OMF is:

[0093]

[0094] As a preferred embodiment of the present invention, step 8, which involves introducing a weighted least squares method into the new orthogonal matched filtering method obtained in step 7, includes:

[0095] Step 8.1.1: Perform weighted least squares filtering on the image after whitening weighted filtering:

[0096]

[0097] In equation (31), u is the filtered image obtained by solving, λ is the regularization parameter, and D x D y For discrete difference operators, A x A y It is a diagonal matrix;

[0098] Step 8.1.2: Differentiate equation (31) above to obtain the minimum solution of u:

[0099] u=(I+λL yOMF ) -1 y OMF (32)

[0100] In equation (32), It is a Laplacian matrix;

[0101] Thus, the final result of u is the output of the orthogonal matched filtering-weighted least squares method.

[0102] Compared with existing technologies, this invention provides a mangrove forest extraction method based on orthogonal matched filtering and weighted least squares, which has the following beneficial effects:

[0103] 1. This method is based on orthogonal subspace projection (OSP), matched filter (MF), and weighted least squares filtering (WLS) methods. It incorporates whitening, regularization, and other optimization techniques to construct an orthogonal matched filter-weighted least squares method. This method enhances the target information of mangroves and reduces background information. The Otsu method is used for threshold segmentation, and the extraction results are displayed through binarization. Finally, it is calibrated and verified through various indicators. It has the advantages of low cost, high accuracy, and short processing time. It solves the problems of high labor cost and low efficiency, insufficient representativeness and coverage of neural network methods, inability to effectively identify and extract mangroves in various complex backgrounds, and low adaptability and accuracy of existing technologies.

[0104] 2. This method uses orthogonal matched filtering-weighted least squares to identify and extract mangrove features, which can effectively identify and extract mangroves under various complex backgrounds, and has the advantages of good adaptability and high accuracy.

[0105] 3. Unlike machine learning, this method only requires traditional mathematical calculations on the target spectral information, without the need for extensive learning and training, and is fast and efficient.

[0106] 4. This method, through the design of a reasonable weighting mechanism, can better handle complex situations under different backgrounds and reduce false identification and false positives. At the same time, the edges of mangroves usually have obvious contrast with the surrounding environment. The method of this invention can effectively preserve these edge features while smoothing the internal information of large areas of mangroves in the image. This makes the extraction of mangrove boundaries clearer and more accurate, and can provide more reliable technical support for the monitoring and protection of mangrove resources. Attached Figure Description

[0107] Figure 1 This is a flowchart of the mangrove extraction method based on orthogonal matched filtering and weighted least squares according to the present invention.

[0108] Figure 2 These are the three mangrove areas selected on the map for this invention;

[0109] Figure 3 For the present invention in Figure 2 The original image of the preprocessed large-scale region A, which is selected in the center box;

[0110] Figure 4 For the present invention in Figure 2 The original image of the preprocessed mesoscale region B, which is selected in the center box;

[0111] Figure 5 For the present invention in Figure 2 The original image of the preprocessed small-scale region C, which is selected in the center box;

[0112] Figure 6 This is an image showing the enhancement effect of the method of the present invention on mangroves before the weighted least squares method filtering;

[0113] Figure 7 This is an image showing the enhancement effect of the method of the present invention on mangroves after filtering using the weighted least squares method;

[0114] Figure 8 The method of this invention is different from other methods. Figure 7 The binarized comparison image is based on the threshold segmentation method of Otsu.

[0115] Among them, Figure 6 In the figure, Figure (a) shows the enhancement effect of the mangrove forest in region A before the weighted least squares method filtering, Figure (b) shows the enhancement effect of the mangrove forest in region B before the weighted least squares method filtering, and Figure (c) shows the enhancement effect of the mangrove forest in region C before the weighted least squares method filtering.

[0116] exist Figure 7 In the figure, Figure (a) shows the enhancement effect of the mangrove forest in region A after filtering by the weighted least squares method, Figure (b) shows the enhancement effect of the mangrove forest in region B after filtering by the weighted least squares method, and Figure (c) shows the enhancement effect of the mangrove forest in region C after filtering by the weighted least squares method.

[0117] exist Figure 8 In the middle, Figure (a) shows the present invention in Figure 2 The original image of region A in the middle, Figure (b) shows the invention in Figure 2 The truth map of region A in the middle, Figure (c) shows the invention in Figure 2 The extraction diagram of the orthogonal matched filter-weighted least squares (OMF-WLS) method for region A in the middle, Figure (d) shows the extraction diagram of the present invention in the middle region A. Figure 2 The matched filter (MF) extraction diagram of region A in the middle, Figure (e) shows the method of the present invention. Figure 2 The constrained energy minimization (CEM) extraction map of region A in the middle, Figure (f) shows the invention in Figure 2 The adaptive coherence estimator (ACE) extraction map for region A in the middle, Figure (g) shows the results of the present invention. Figure 2 Maximum likelihood estimation (MLE) extraction map of region A in the middle, Figure (h) shows the maximum likelihood estimation (MLE) extraction map of the present invention in region A. Figure 2 The original image of region B in the middle, Figure (i) is the original image of the present invention in the middle region B. Figure 2 The truth map of region B in the middle, Figure (j) shows the invention in Figure 2 The extraction diagram of the orthogonal matched filter-weighted least squares (OMF-WLS) method in region B of the middle region is shown in Figure (k). Figure 2 The matched filter (MF) extraction diagram of region B in the middle, Figure (l) shows the extraction diagram of the matched filter (MF) of the present invention. Figure 2 The constrained energy minimization (CEM) extraction map of region B in the middle, Figure (m) shows the method of the present invention. Figure 2 The adaptive coherence estimator (ACE) extraction diagram for region B in the middle, Figure (n) shows the results of this invention. Figure 2 Maximum likelihood estimation (MLE) extraction map of region B in the middle; Figure (o) shows the maximum likelihood estimation (MLE) extraction map of region B in the present invention. Figure 2 The original image of region C in the middle, Figure (p) shows the invention in Figure 2 The truth map of region C in the middle, Figure (q) shows the invention in Figure 2 The extraction diagram of the orthogonal matched filter-weighted least squares (OMF-WLS) method in region C of the middle region is shown in Figure (r). Figure 2 The matched filter (MF) extraction diagram of region C in the middle, Figure (s) shows the method of the present invention. Figure 2 The constrained energy minimization (CEM) extraction map of region C in the middle, Figure (t) shows the method of the present invention. Figure 2 The adaptive coherence estimator (ACE) extraction diagram for region C in Figure (u) is shown in Figure (u). Figure 2 Maximum likelihood estimation (MLE) extraction map of region C. Detailed Implementation

[0118] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0119] Example 1:

[0120] Please refer to the instruction manual appendix. Figure 1 - Appendix Figure 8 The present invention provides a technical solution:

[0121] A mangrove forest extraction method based on orthogonal matched filtering-weighted least squares includes:

[0122] Step 1: Acquire the original multispectral remote sensing image and preprocess and fuse the remote sensing image. The specific process includes:

[0123] Step 1.1: Please refer to the attached document. Figure 2 Select three regions (see appendix) Figure 3 Appendix Figure 4 Appendix Figure 5 The original multispectral remote sensing images were obtained and preprocessed.

[0124] The preprocessing procedure for raw multispectral remote sensing images includes radiometric calibration, atmospheric correction, and orthorectification.

[0125] Step 1.2: After preprocessing the original multispectral remote sensing image, the multispectral image and the panchromatic image are fused to obtain a high-resolution multispectral fused remote sensing image.

[0126] The fusion method used for image fusion is the Gram-Schmidt (GS) method.

[0127] Step 2: In order to eliminate interference from the ocean, the multispectral fused remote sensing image is separated into land and sea areas;

[0128] The process of separating land and sea in multispectral fused remote sensing images includes: first, editing the vector features of the multispectral fused remote sensing images using embedded GIS (ArcGIS), and finally performing masking processing.

[0129] Step 3: After separating the land and sea in the multispectral fused remote sensing image, the average spectrum of the prior information is obtained from the spectral library based on the spectral information of the mangroves collected multiple times.

[0130] The spectral library is a .sli file obtained using ENVI, which is then imported into MATLAB and converted into matrix form.

[0131] Step 4: By expanding the bands, construct characteristic indices to enhance the spectral characteristics of the target, and further distinguish mangroves using the characteristic indices;

[0132] The constructed characteristic indices include four indices: Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), Normalized Difference Water Index (NDWI), and Total Suspended Solids Concentration Index (TSM).

[0133] Step 5: Perform two-dimensional and normalization processing on the remote sensing image data to complete data preprocessing. The specific process includes:

[0134] Step 5.1: Convert the 3D multispectral image into a 2D matrix and map the data to between 0 and 1 to remove the dimensions and units of the data from different dimensions;

[0135] Step 5.2: Next, perform average normalization on the data to center the data at 0, and then standardize the data to place the features on the same proportion; the known covariance matrix is:

[0136]

[0137] Since the data has been normalized to the mean, the mean is... Therefore, equation (1) can be transformed into:

[0138]

[0139] Then, eigenvalue decomposition is performed on the covariance matrix C to calculate the eigenvalues ​​and eigenvectors, resulting in:

[0140] C = UAU T (3)

[0141] In equation (3), U is the eigenvector, Λ is the diagonal matrix, and the elements on the diagonal are the eigenvalues;

[0142] Step 6: Based on the orthogonal subspace projection and matched filter method, add whitening and regularization terms and other optimization operations to the remote sensing image data processed in Step 5;

[0143] The solution processes for orthogonal subspace projection and matched filter methods include:

[0144] Step 6.1: The solution process for Orthogonal Subspace Projection (OSP) is as follows:

[0145] Step 6.1.1: First, let X be an L×1 dimensional pixel spectral vector, and K represent the dimension of the endmember spectral matrix, where α i This represents the abundance of the corresponding endmember, expressed as:

[0146]

[0147] The OSP model consists of the target signal d and the background endmember U. Therefore, we can obtain:

[0148]

[0149] In equation (5), Let be the abundance vector of the target signal. is the abundance vector of background endmembers, and n is the noise or model error;

[0150] Step 6.1.2: In order to extract the target signal of interest while suppressing all other background features, an orthogonal subspace projector is introduced, where ⊥ represents the orthogonal complement space, defined as follows:

[0151]

[0152] The constructed filter detector can be described as follows:

[0153]

[0154] In equation (6), I is a K×K dimensional identity matrix, (U T U) -1 U T Let U be the pseudo-inverse of matrix U, where U T This represents the transpose of the U matrix; as shown in equation (7), prior knowledge of image endmembers is required when performing endmember extraction.

[0155] Step 6.2: The solution process for the Matched Filter (MF) method is as follows:

[0156] Step 6.2.1: Assuming the image to be identified has B bands, the vector form of each pixel can be expressed as:

[0157] x s = [x1, x2, x3, ..., x B ] T (s=1,2,3,…,S) (8)

[0158] In equation (8), S = LEN × WID, where LEN is the length of the image size and WID is the width of the image size. Each band of the sensor will obtain a grayscale image G of size S. b :

[0159] G b (len,wid)(b=1,2,3,…,B; len=1,2,3,…,LEN; wid=1,2,3,…,WID) (9)

[0160] Step 6.2.2: The 3D image data can be rearranged as follows:

[0161] X = [x1, x2, x3, ..., x S (10)

[0162] Therefore, it can be expressed as:

[0163] X(b,s)(b=1,2,3,…,B; s=1,2,3,…,S) (11)

[0164] The relationship between equation (9) and equation (11) is as follows:

[0165] G b (len,wid)=X(b,(len-1)WID+wid) (12)

[0166] Step 6.2.3: Based on the known prior information, the matched filter (MF) algorithm for single-target detection can be reduced to a simple quadratic programming problem:

[0167]

[0168] In equation (13), μ1 is the mean vector of the target pixel, μ0 is the mean vector of the background pixel, and W is a linear filter. By introducing the Lagrange multiplier method, the unknown vector W can be solved:

[0169]

[0170] Background covariance matrix and background mean vector Estimate based on existing data:

[0171]

[0172] The linear detector takes the form of:

[0173]

[0174] The target mean vector is obtained by averaging existing spectral libraries or tag information:

[0175]

[0176] Step 6.2.4: Combine the data from equations (14)-(18) to perform Mahalanobis distance calculation between the target and the background, and finally obtain:

[0177]

[0178] Step 6.3: The process of adding whitening and regularization terms to the remote sensing image data processed in Step 5 includes:

[0179] Step 6.3.1: By combining the features x of each dimension rot，i Divide by the square root of its corresponding eigenvalue To scale our decorrelated data, we obtain the data matrix after PCA whitening:

[0180]

[0181] Sometimes we encounter eigenvalues ​​λ i The case of values ​​very close to 0. This can cause numerical instability or overflow when dividing a value by a number close to zero. To address this issue, the eigenvalues ​​are scaled, and a small constant ε is added to ensure that division by values ​​close to zero is avoided; typically, ε ≈ 10. -5 This constant is usually called the regularization term. Adding this constant ensures that numerical instability or overflow issues are avoided during division operations. Therefore, the final result of the PCA whitening matrix is:

[0182]

[0183] Step 6.3.2: Combining equations (5)-(7) and equation (21) to perform whitening weighted calculations to obtain:

[0184]

[0185] Therefore, the detector can be redefined as:

[0186]

[0187] Step 6.3.3: Finally, for the orthogonal subspace projector in equation (23) By constructing a sparse matrix, target information is effectively enhanced while background information is suppressed, resulting in a whitened sample space as follows:

[0188]

[0189] Therefore, MF can be rewritten as:

[0190]

[0191] In equation (25), It is a constant;

[0192] Step 7: By combining the orthogonal subspace projection and matched filter method optimized in Step 6, a new method, the orthogonal matched filtering method, is obtained. The specific process includes:

[0193] Step 7.1: First, a new measurement method is used to find the projection vector W. In the whitening space, W can be found by minimizing it, and a new output is obtained:

[0194]

[0195] Step 7.2: Next, change d in equation (22) white As the target vector in the matched filter A new Orthogonal Matching Filter (OMF) optimization model is formed, and the constrained minimization problem becomes:

[0196]

[0197] Step 7.3: Finally, expand and simplify the model as follows:

[0198]

[0199] In equation (28), ∑ OMF This represents the autocovariance matrix of the weighted whitened samples. In the whitening space, the covariance matrix is ​​the identity matrix. Solving this model yields:

[0200]

[0201] Therefore, the final output of OMF is:

[0202]

[0203] Step 8: In the new orthogonal matched filtering method obtained in step 7, a weighted least squares method is introduced to obtain the final method of this embodiment - a mangrove extraction method based on orthogonal matched filtering and weighted least squares. Finally, the Otsu method is used for threshold segmentation to realize the mangrove identification and extraction process.

[0204] Step 8.1: In the new orthogonal matched filtering method, the weighted least squares method (Maximum Likelihood Estimation, MLE) is introduced. The process of obtaining the mangrove extraction method based on orthogonal matched filtering-weighted least squares includes:

[0205] Step 8.1.1: Perform weighted least squares filtering on the image after whitening weighted filtering:

[0206]

[0207] In equation (31), u is the filtered image obtained by solving, and λ is the regularization parameter used to balance u and y. OMF The weighting between the two factors is important. When the edge gradient changes of the input image are large, we want the constraint to be smaller to preserve the structural information of the image; when the edge gradient changes of the image are small, we consider this detailed information unimportant, and the constraint can naturally be larger. x D y For discrete difference operators, A x A y It is a diagonal matrix;

[0208] Step 8.1.2: By differentiating equation (31) above, the minimum value of u is obtained as follows:

[0209] u=(I+λL yOMF ) -1 y OMF (32)

[0210] In equation (32), It is a Laplacian matrix; thus, the final result of u is the output of the Orthogonal Matching Filter-Weighted Least Squares (OMF-WLS) method verified in this embodiment;

[0211] Step 8.2: Please refer to the appendix. Figure 8 The filtered u-image will be binarized and segmented based on the Otsu method to achieve accurate extraction of mangrove targets.

[0212] Example 2:

[0213] As per the instruction manual Figure 1 - Appendix Figure 8 As shown, this embodiment is designed to verify the feasibility of the mangrove extraction method based on orthogonal matched filtering-weighted least squares as described in Example 1:

[0214] 1. Experimental Procedure

[0215] Using the method described in step 4 of Example 1, the spectral characteristics of mangroves are constructed and enhanced using a method that utilizes characteristic indices to reflect and extract the land cover features of mangroves. These characteristic indices are typically new image data obtained by mathematically operating and combining different bands in remote sensing images, used to reflect certain attributes or conditions of surface features. The characteristic indices constructed in this invention are mainly divided into two categories: one is vegetation indices, which mainly reflect the growth status and coverage of vegetation by combining infrared and visible light bands. Common vegetation indices include the Normalized Difference Vegetation Index (NDVI). These indices can effectively distinguish mangroves from background information because mangroves usually have high vegetation coverage. The second category is water body indices, which mainly reflect the distribution and type of water bodies by combining blue light and near-infrared bands. Common water body indices include the Normalized Difference Water Index (NDWI). These indices can effectively distinguish between water bodies and land because water body indices usually have higher values ​​in water bodies and lower values ​​in land areas.

[0216] Since the PCA bleaching method described in Embodiment 1 of this invention is based on singular value decomposition (SVD), to avoid highly correlated features in the input data leading to singular values ​​close to zero in the SVD results, or even overfitting, this embodiment will only select four indices: NDVI (Normalized Difference Vegetation Index), EVI (Enhanced Vegetation Index), NDWI (Normalized Difference Water Index), and TSM (Total Suspended Solids Index). These indices will be used to further distinguish mangroves. Finally, after band expansion, there will be 8 bands. Table 1 shows the characteristic indices after band expansion, where B1 represents the blue light band, B2 represents the green light band, B3 represents the red light band, and B4 represents the near-infrared band.

[0217] Table 1: Characteristic Indices After Band Extension

[0218]

[0219] 2. Results Analysis

[0220] To better quantify and evaluate the ability to identify and extract mangroves, this embodiment randomly selects samples from the research subjects in the Yingluo Port area, averages these samples to obtain prior information about the target, and then uses ENVI to export a spectral library. Based on the selected sample data, a confusion matrix is ​​used to calculate four indicators for mangroves: Overall Accuracy (OA), Average Accuracy (AA), Producer's Accuracy (PA), and Kappa coefficient. The formulas are as follows:

[0221]

[0222] In this context, TP (True Positive) represents the number of true positive instances, which are predicted as positive by the model and are actually labeled as positive; TN (True Negative) represents the number of true negative instances, which are predicted as negative by the model and are actually labeled as negative; FP (False Positive) represents the number of false positive instances, which are predicted as positive by the model but are actually labeled as negative; and FN (False Negative) represents the number of false negative instances, which are predicted as negative by the model but are actually labeled as positive.

[0223] Therefore, through the above experiments... Figure 8 Comparing the mangrove identification and extraction results before and after calibration with other methods using the method described in Example 1 of this invention, it can be seen that the method described in Example 1 of this invention can effectively improve the mangrove identification and extraction effect. (The appendix is ​​missing from the original text.) Figure 8 (a) - Figure (g) represents the original image, ground truth map, orthogonal matched filter-weighted least squares (OMF-WLS) extraction map, matched filter (MF) extraction map, constrained energy minimization (CEM) extraction map, adaptive coherence estimator (ACE) extraction map, and maximum likelihood estimation (MLE) extraction map for region A. Similarly, the attached figures... Figure 8 (h)-(n) and Figure 8 (o)-(u) represent the extraction results of different methods for regions B and C with the same arrangement order as region A.

[0224] Finally, these indices (Tables 2, 3, and 4) were used to quantitatively evaluate the extraction effect of mangroves, with values ​​closer to 1 indicating better results.

[0225] Table 2: Extraction Results and Indicators for Area A of Yingluo Port

[0226]

[0227] Table 3: Extraction Results and Indicators for Region B of Yingluo Port

[0228]

[0229]

[0230] Table 4: Extraction Results and Indicators of Region C in Yingluo Port

[0231]

[0232] Therefore, it is demonstrated that the method described in Embodiment 1 of the present invention achieves an accuracy of over 94% for all indicators, whether in large-scale or small-scale regions. Furthermore, regardless of the complexity of the background, the method described in Embodiment 1 of the present invention exhibits a stable and superior performance in extracting and identifying mangroves compared to other methods.

[0233] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0234] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A mangrove forest extraction method based on orthogonal matched filtering-weighted least squares, characterized in that: include: Step 1: Acquire the original multispectral remote sensing images and preprocess and fuse them; Step 2: Perform land-sea separation processing on the multispectral fused remote sensing image; Step 3: After separating the land and sea in the multispectral fused remote sensing image, the average spectrum of the prior information is obtained from the spectral library based on the spectral information of the mangroves collected multiple times. Step 4: After obtaining prior information, feature indices are constructed through band expansion, and mangroves are further distinguished through feature indices; Step 5: Perform two-dimensionalization and normalization on the remote sensing image data obtained in Step 4; Step 5, which involves adding whitening and regularization terms to the remote sensing image data, includes: Step 6.3.1: By combining the features of each dimension Divide by the square root of its corresponding eigenvalue Scaling the data yields a PCA-whitened data matrix: (20) Add a regularization term constant to the data matrix The final result of obtaining the PCA whitening matrix is: (21) Step 6.3.2: Perform whitening weighted operations on equations (5)-(7) and (21) to obtain: (22) Therefore, the detector is redefined as: (23) Step 6.3.3: Project the orthogonal subspace in equation (23) Constructing a sparse matrix yields the whitened sample space as follows: (24) Therefore, MF is rewritten as: (25) In equation (25), It is a constant; Step 6: Based on the orthogonal subspace projection and matched filter method, add whitening and regularization terms to the remote sensing image data processed in Step 5; Step 7: By combining the orthogonal subspace projection and matched filter method optimized in Step 6, a new orthogonal matched filtering method is obtained; Step 8: Introduce the weighted least squares method into the new orthogonal matched filtering method obtained in step 7 to obtain a mangrove extraction method based on orthogonal matched filtering-weighted least squares. Finally, use the Otsu method for threshold segmentation to realize the identification and extraction of mangroves.

2. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: Step 1 describes the process of preprocessing and fusing remote sensing images, which includes: Step 1.1: Select the area to be acquired and obtain the original multispectral remote sensing image of the area, and preprocess the image; The preprocessing procedure for raw multispectral remote sensing images includes radiometric calibration, atmospheric correction, and orthorectification. Step 1.2: After preprocessing the original multispectral remote sensing image, the multispectral image and the panchromatic image are fused to obtain a high-resolution multispectral fused remote sensing image. The image fusion method used is the Gram-Schmidt method.

3. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: When performing land-sea separation processing on the multispectral fused remote sensing image as described in step 2, the vector elements of the multispectral fused remote sensing image are first edited using embedded GIS, and then masking is performed.

4. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: The characteristic indices mentioned in step 4 include the normalized vegetation index, enhanced vegetation index, normalized differential water body index, and total suspended solids concentration index.

5. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: Step 5 describes the process of performing two-dimensionalization and normalization on the remote sensing image data, which includes: Step 5.1: Convert the 3D multispectral image into a 2D matrix and map the data to between 0 and 1, removing the dimensions and units of the data from different dimensions; Step 5.2: Next, perform average normalization on the data to center the data at 0, and then standardize the data; the specific process is as follows: Given the covariance matrix: ； Since the data has been normalized to the mean, Therefore, equation (1) is transformed into: （2） Then, the covariance matrix... By performing eigenvalue decomposition and calculating eigenvalues ​​and eigenvectors, we have: （3） In equation (3), For feature vectors, It is a diagonal matrix, and the elements on the diagonal are the eigenvalues.

6. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: Step 5 describes the solution process using the orthogonal subspace projection method, which includes: Step 6.1.1: First, let's assume... for 3D pixel spectral vector, The dimension representing the endmember spectral matrix, The abundance of the corresponding endmember is represented by the expression: (4) The OSP model consists of the target signal. and background end element Composition, therefore we get: (5) In equation (5), Let be the abundance vector of the target signal. This is the abundance vector of background endmembers. This could be noise or model error; Step 6.1.2: Introduce an orthogonal subspace projector, defined as: （6） In equation (6), To fill the orthogonal space, for An identity matrix of dimension 1 for The pseudo-inverse of a matrix. Representative to Transpose the matrix; The constructed filter detector is as follows: (7)。 7. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: Step 5 describes the solution process for the matched filter method, which includes: Step 6.2.1: Suppose the image to be identified has... Each pixel in each band has a vector form as follows: (8) In equation (8), , The length of the image size. Given the width of the image size, the sensor in each band will obtain a size of... grayscale image : (9) Step 6.2.2: Rearrange the 3D image data as follows: (10) The expression is as follows: (11) The relationship between equation (9) and equation (11) is as follows: (12) Step 6.2.3: Based on prior information, reduce the matched filter algorithm for single-target detection to a quadratic programming problem: (13) In equation (13), Let be the mean vector of the target pixel. The mean vector of the background pixels. It is a linear filter; Introducing the Lagrange multiplier method for unknown vectors Solve the following: (14) Background covariance matrix and background mean vector Based on existing data, it is estimated that: (15) (16) The linear detector takes the form of: (17) The target mean vector is obtained by averaging existing spectral libraries or label information: (18) Step 6.2.4: Combining the data from equations (14) to (18), perform Mahalanobis distance calculation between the target and the background to obtain: (19)。 8. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: Step 7, which combines the orthogonal subspace projection and matched filter method optimized in step 6 to obtain the orthogonal matched filter method, includes the following steps: Step 7.1: First, use the new measurement method to find the projection vector. In the whitened space, Find it by minimizing it, and obtain the new output: (26) Step 7.2: Next, in equation (22) As the target vector in the matched filter This leads to a new orthogonal matched filter optimization model, and the constraint minimization problem becomes: (27) Step 7.3: Finally, the new orthogonal matched filter optimization model is expanded and simplified as follows: (28) In equation (28), Let represent the autocovariance matrix of the weighted whitened samples. In the whitening space, the covariance matrix is ​​the identity matrix. Solving the new orthogonal matched filter optimization model yields: (29) Therefore, the final output of OMF is: (30)。 9. The mangrove forest extraction method based on orthogonal matched filtering-weighted least squares as described in claim 1, characterized in that: Step 8 describes the process of introducing a weighted least squares method into the new orthogonal matched filtering method obtained in step 7, which includes: Step 8.1.1: Perform weighted least squares filtering on the image after whitening weighted filtering: (31) In equation (31), The filtered image obtained by solving, For regularization parameters, , For discrete difference operators, , It is a diagonal matrix; Step 8.1.2: Differentiate the above equation (31) to obtain The minimum solution is: (32) In equation (32), It is a Laplacian matrix; Thus, the final The result is the output of the orthogonal matched filtering-weighted least squares method.

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