A time-series insar statistical homogenous pixel selection method, system and device

Abstract

The application provides a time sequence InSAR statistical homogenous pixel selection method, system and device, and belongs to the technical field of distributed scatterer InSAR, and the method comprises the following steps: obtaining reference pixels and a set of to-be-detected pixels of N time sequence SAR intensity images based on a target window; calculating the time sequence average intensity of the SAR intensity images, and obtaining a preliminary candidate pixel set of the reference pixels by using a F distribution confidence interval; determining the estimated value of the reference pixels by jointly considering the gray difference and the similarity weight adjustment mechanism of the spatial position based on the preliminary candidate pixel set; determining the statistical homogenous pixel set of the reference pixels in the preliminary candidate pixel set by using a gamma distribution confidence interval based on the estimated value of the reference pixels; and screening the pixels in the statistical homogenous pixel set by using a spatial consistency test algorithm to obtain the target statistical homogenous pixel of the reference pixels. The application can improve the accuracy and effectiveness of homogenous pixel selection.

Description

Technical Field

[0001] This application belongs to the field of distributed scatterer InSAR technology, and more specifically, it relates to a method, system and device for selecting statistical homogeneous pixels in time-series InSAR. Background Technology

[0002] Time Series Interferometric Synthetic Aperture Radar (TS-InSAR), a high-precision remote sensing technique, has been widely applied in fields such as land surface deformation monitoring. Traditional TS-InSAR methods rely on the high coherence characteristics of permanent scatterers (PS), resulting in monitoring blind spots in low-coherence areas such as farmland, water bodies, and bare land. To improve monitoring coverage in low-coherence areas, the Distributed Scatterer (DS) model was proposed, leading to the development of Distributed Scatterer Target InSAR technology (DS-InSAR), which has become a hot topic in current InSAR research.

[0003] In DS-InSAR technology, the selection of statistically homogeneous pixels (SHPs) is a crucial step, directly affecting the accuracy of subsequent phase optimization and deformation inversion. Currently, most mainstream SHP identification methods are based on hypothesis testing theory, primarily including non-parametric and parametric tests. Non-parametric tests, such as the KS test and BWS test, select SHPs by comparing differences in sample distributions, exhibiting distribution independence but lower computational efficiency. Parametric tests, on the other hand, select SHPs by performing significance analysis on sample statistics under the assumption that the samples follow a certain statistical distribution. In recent years, researchers have proposed confidence interval-based parametric test methods, such as the Hypothesis Test of Confidence Interval (HTCI) algorithm, which improves computational efficiency compared to non-parametric methods but ignores the impact of local structural changes in the image on SHP extraction. Therefore, regardless of whether non-parametric or parametric methods are used, a more accurate and effective method for selecting homogeneous pixels is still lacking.

[0004] In summary, providing an accurate and effective method for selecting homogeneous pixels is one of the key technical challenges that DS-InSAR technology urgently needs to address. Summary of the Invention

[0005] The purpose of this application is to provide a method, system, and device for selecting homogeneous pixels in time-series InSAR statistics, so as to solve the limitations of existing homogeneous pixel selection methods in handling local heterogeneity and relying on global statistical features, thereby improving the accuracy and effectiveness of homogeneous pixel selection.

[0006] A first aspect of this application provides a method for selecting statistically homogeneous pixels in temporal InSAR, including:

[0007] Based on the target window, obtain the reference pixels and the set of pixels to be detected for N time-series SAR intensity images;

[0008] Calculate the time series average intensity of N time series SAR intensity images. Based on the time series average intensity, construct the F-distribution information interval of the reference pixel using the F-distribution to obtain the preliminary candidate pixel set of the reference pixel. The candidate pixels in the preliminary candidate pixel set belong to the pixel set to be detected.

[0009] Based on the preliminary candidate pixel set, the estimated value of the reference pixel is determined by using the gray-scale similarity weight between the candidate pixel and the reference pixel, and the spatial similarity weight between the candidate pixel and the reference pixel.

[0010] Based on the estimated values ​​of the reference pixels, the gamma distribution confidence interval is used to determine the statistically homogeneous set of pixels in the preliminary candidate pixel set and the reference pixel set.

[0011] The target statistically homogeneous pixels for reference pixels are obtained by filtering pixels in a statistically homogeneous pixel set using a spatial consistency test algorithm.

[0012] A second aspect of this application provides a temporal InSAR statistical homogeneous pixel selection system, comprising:

[0013] The acquisition unit is used to acquire reference pixels and a set of pixels to be detected for N time-series SAR intensity images based on the target window;

[0014] The first processing unit is used to calculate the time series average intensity of N time series SAR intensity images. Based on the time series average intensity, the F distribution information interval of the reference pixel is constructed using the F distribution to obtain the preliminary candidate pixel set of the reference pixel. The candidate pixels in the preliminary candidate pixel set belong to the pixel set to be detected.

[0015] The weight calculation unit is used to determine the estimated value of the reference pixel based on the preliminary candidate pixel set, using the gray-level similarity weight between the candidate pixel and the reference pixel, and the spatial similarity weight between the candidate pixel and the reference pixel.

[0016] The second processing unit is used to determine the statistically homogeneous set of the preliminary candidate pixel set and the reference pixel set based on the estimated value of the reference pixel and the gamma distribution information interval.

[0017] The filtering unit is used to filter the pixels in the statistically homogeneous pixel set to obtain the target statistically homogeneous pixels of the reference pixels using the spatial consistency test algorithm.

[0018] A third aspect of this application provides an electronic device, including a memory, a processor, and a computer program stored in the memory and running on the processor, wherein the processor executes the computer program to implement the steps of the above-described temporal InSAR statistical homogeneous pixel selection method.

[0019] A fourth aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described temporal InSAR statistical homogeneous pixel selection method.

[0020] The beneficial effects of the temporal InSAR statistical homogeneous pixel selection method, system, and device provided in this application are as follows:

[0021] This application embodiment determines reference pixels and pixels to be detected through a target window, and constructs the F-distribution confidence interval of the reference pixels using the F-distribution, thereby filtering the pixels to be detected to obtain candidate pixels. This application embodiment also effectively improves the representation ability of local structures and overall robustness in the reference pixel estimation process by jointly considering the gray-level similarity weight and spatial similarity weight between candidate pixels and reference pixels. Compared with the prior art, this application embodiment not only enhances the adaptability to local heterogeneity, but also significantly reduces the estimation bias caused by local noise or structural perturbations. In addition, based on the obtained estimated value of the reference pixels, this application embodiment uses the gamma distribution confidence interval to filter and obtain a set of statistically homogeneous pixels for the reference pixels. Finally, it uses a spatial consistency test algorithm to verify the spatial consistency of the pixels in the set of statistically homogeneous pixels, obtaining the final target statistically homogeneous pixels for the reference pixels. This application embodiment further improves the accuracy and effectiveness of homogeneous pixel selection through the above multiple steps. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1A flowchart illustrating a method for selecting statistical homogeneous pixels in temporal InSAR according to an embodiment of this application;

[0024] Figure 2 This is a schematic diagram of N time-series SAR intensity images provided in an embodiment of this application;

[0025] Figure 3 This is a schematic diagram illustrating the statistical analysis of homogeneous pixels for a reference pixel p according to an embodiment of this application.

[0026] Figure 4 A schematic diagram of statistical homogeneous pixels, optimized interferometric phase, and posterior coherence of simulation data provided in an embodiment of this application under different methods;

[0027] in, Figure 4 (a) From bottom to top, the comparison results of statistical homogeneous pixel identification for WAHTCI, HTCI, GLRT, BWS and KS methods, as well as high-noise data and noise-free data;

[0028] Figure 4 (b) From bottom to top, the results are the comparison of the optimized interferometric phase recovery of the WAHTCI, HTCI, GLRT, BWS and KS methods, as well as the results of high-noise data and noise-free data.

[0029] Figure 4 (c) From bottom to top, the comparison results of posterior coherence of WAHTCI, HTCI, GLRT, BWS and KS methods, as well as high-noise data and noise-free data;

[0030] Figure 5 The number of statistically homogeneous pixels identified at the center pixel under different methods in simulation data provided in an embodiment of this application;

[0031] Figure 6 A schematic diagram illustrating the average efficacy of different methods provided in an embodiment of this application under multiple parameter ratios;

[0032] Figure 7 A schematic diagram illustrating the standard deviation of the efficacy of different methods provided in an embodiment of this application under multiple parameter ratios;

[0033] Figure 8 A partially enlarged schematic diagram showing the average efficacy of different methods provided in an embodiment of this application under multiple parameter ratios;

[0034] Figure 9 A partially enlarged schematic diagram showing the standard deviation of the efficacy of different methods provided in an embodiment of this application under multiple parameter ratios;

[0035] Figure 10A structural block diagram of a temporal InSAR statistical homogeneous pixel selection system provided in an embodiment of this application;

[0036] Figure 11 This is a schematic block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0037] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0038] To make the objectives, technical solutions, and advantages of this application clearer, the following description will be provided in conjunction with the accompanying drawings and specific embodiments.

[0039] Please refer to Figure 1 , Figure 1 This is a flowchart illustrating a method for selecting homogeneous pixels in temporal InSAR statistics according to an embodiment of this application. The method can be executed by an electronic device and may include steps S101-S105.

[0040] S101: Obtain the reference pixels and the set of pixels to be detected for N time-series SAR intensity images based on the target window.

[0041] In this embodiment, N time-series SAR intensity images can represent N SAR intensity images acquired at N different time points for the same area, where N can be 31. In this embodiment, simulation data is acquired, which includes N time-series SAR intensity images. The intensity data in the N time-series SAR intensity images is read using the following formula, and the pixel size of the N time-series SAR intensity images is 360×500.

[0042] .

[0043] in, L represents the original single-look complex image of SAR, where L is the number of spatial samples, also known as the original number of SAR views.

[0044] Based on acquiring N time-series SAR intensity images, a target window is set, which can be the first window with a size of 7×7. The pixel located at the center of the first window is determined as the reference pixel p, and the set of pixels other than the reference pixel that are located within the first window is taken as the set of pixels to be detected.

[0045] S102: Calculate the time series average intensity of N time series SAR intensity images. Based on the time series average intensity, construct the F-distribution information interval of the reference pixels using the F-distribution to obtain the preliminary candidate pixel set of the reference pixels.

[0046] The candidate pixels in the preliminary candidate pixel set belong to the pixel set to be detected.

[0047] In one embodiment, based on the reference pixel and the pixel to be detected obtained in S101, the time series average intensity of the reference pixel p and the pixel to be detected q under the first window are calculated respectively. Based on the time series average intensity of the reference pixel p and the time series average intensity of the pixel to be detected q, the F-distribution confidence interval of the reference pixel is constructed using the F-distribution to obtain the preliminary candidate pixel set of the reference pixel.

[0048] If N original SAR images follow a complex circular Gaussian distribution in the time dimension, then N time-series SAR intensity images I follow an exponential distribution. Therefore, the probability density function of N time-series SAR intensity images I can be expressed as: .in, It is a parameter of the exponential distribution.

[0049] Based on the relationship between the exponential distribution and the gamma distribution, N time-series SAR intensity images I satisfy a shape parameter of 1 and a scale parameter of... The gamma distribution, i.e. For a dataset of N time-series SAR intensity images I1, I2, ..., IN, based on the relationship and properties of the gamma and chi-square distributions, for a reference pixel p and a pixel to be detected q, we have:

[0050] .

[0051] in, and These are the temporal numbers of the reference pixel p and the pixel to be detected q, respectively. , Reference pixels Time series average intensity, pixels to be detected The time series average intensity, F() represents the F distribution. Since ,but The ratio follows an F-distribution with (2N, 2N) degrees of freedom. Therefore, the confidence interval of the F-distribution can be expressed as:

[0052] .

[0053] In the formula, Represents probability. At the significance level, for The upper quantile of the distribution, for The lower quantile of the distribution , Reference pixels Time series average intensity, pixels to be detected The average intensity of the time series.

[0054] In this embodiment, The pixels to be detected within the distributed signal interval are used as reference pixels. Preliminary candidate pixel set , This represents the set of pixels to be detected.

[0055] S103: Based on the preliminary candidate pixel set, the estimated value of the reference pixel is determined by using the gray-scale similarity weight between the candidate pixel and the reference pixel, and the spatial similarity weight between the candidate pixel and the reference pixel.

[0056] In one embodiment, the gray-level Euclidean distance between the candidate pixel and the reference pixel in the time series is calculated, and gray-level similarity weights are constructed based on the Gaussian kernel function and the gray-level Euclidean distance. Specifically, the square of the gray-level Euclidean distance between the candidate pixel and the reference pixel in the time series can be calculated based on the following formula:

[0057] .

[0058] Where i represents the time series index, i.e., the phase number, i = 1, 2, ..., N; This represents the intensity value of candidate pixel q in the i-th time phase; This represents the intensity value of reference pixel p in the i-th time phase; This represents the square of the gray-level Euclidean distance between the candidate pixel and the reference pixel in the time series.

[0059] In this embodiment, the gray-level Euclidean distance directly measures the distance between the reference pixel and the candidate pixel in the gray-level space. The smaller the distance, the closer the gray-level values ​​are, and the higher the similarity. However, the gray-level Euclidean distance simply calculates the numerical difference and does not consider that in practical applications, the impact of different degrees of gray-level differences on similarity may not be linear, and it has poor robustness to factors such as noise. Based on this, this embodiment introduces a Gaussian kernel function to perform a nonlinear transformation on the gray-level Euclidean distance to obtain gray-level similarity weights.

[0060] In one embodiment, gray-level similarity weights are constructed based on a Gaussian kernel function and gray-level Euclidean distance, including:

[0061] The gray-level similarity weights are constructed based on the following formula:

[0062] .

[0063] in, For grayscale similarity weights, This is the mean of the squared gray-level Euclidean distances of all candidate pixels. This is a preliminary candidate pixel set. Let be the square of the gray-level Euclidean distance of all candidate pixels. It is an exponential function with the natural constant e as its base.

[0064] In one embodiment, the spatial Euclidean distance between the candidate pixel and the reference pixel in terms of spatial location is calculated, and a spatial similarity weight is constructed based on the spatial decay function and the spatial Euclidean distance. Specifically, the square of the spatial Euclidean distance between the candidate pixel and the reference pixel in the time series can be calculated based on the following formula: .

[0065] in, Candidate pixels Two-dimensional spatial position vector, Reference pixel Two-dimensional spatial position vector, It is a 2-norm (Euclidean norm). It is the square of the spatial Euclidean distance between the candidate pixel and the reference pixel in the time series.

[0066] In one embodiment, spatial similarity weights are constructed based on a spatial decay function and spatial Euclidean distance, including:

[0067] Spatial similarity weights are constructed based on the following formula:

[0068] .

[0069] in, For spatial similarity weights, Let be the square of the spatial Euclidean distance of all candidate pixels. It is an exponential function with the natural constant e as its base. It is the square of the largest spatial Euclidean distance among all candidate pixels.

[0070] In one embodiment, after obtaining the gray-scale similarity weight and the spatial similarity weight, the gray-scale similarity weight and the spatial similarity weight can be fused to obtain a joint similarity weight, and the estimated value of the time series average intensity of the reference pixel can be determined based on the joint similarity weight.

[0071] In this embodiment, the joint similarity weight is calculated based on the quantized values ​​of the grayscale similarity weight and the spatial similarity weight. In one embodiment, the joint similarity weight is obtained by fusing the grayscale similarity weight and the spatial similarity weight, including:

[0072] The joint similarity weight is obtained based on the following formula:

[0073] .

[0074] in, To combine similarity weights, For the pixel to be detected, For grayscale similarity weights, For spatial similarity weights, This is the initial candidate pixel set.

[0075] This embodiment addresses the limitations of existing methods in handling local heterogeneity and dependence on global statistical features by introducing a joint weighting mechanism of grayscale similarity weight and spatial similarity weight. It improves the ability to represent local structures during reference pixel estimation and facilitates the subsequent extraction of statistically homogeneous pixels.

[0076] S104: Based on the estimated value of the reference pixel, the statistically homogeneous set of pixels in the preliminary candidate pixel set and the reference pixel is determined by using the gamma distribution confidence interval.

[0077] In this embodiment, after calculating the estimated value of the reference pixel, a second window is set. The size of the second window is larger than that of the first window (target window), for example, it can be set to 15×15. The pixel located at the center of the second window is the reference pixel determined under the first window. Based on the estimated value of the reference pixel... Construct a gamma distribution signal interval, and define the pixels to be detected within the gamma distribution signal interval as the reference pixels. A statistically homogeneous set of pixels.

[0078] The gamma distribution signal interval of the reference pixel is:

[0079] .

[0080] in, Represents probability. At the significance level, The upper quantile of the standard gamma distribution. The lower quantile of the standard gamma distribution Reference pixel The estimated value, The average intensity of the pixels to be detected within the second window is the time series intensity.

[0081] S105: Use the spatial consistency test algorithm to filter the pixels in the statistically homogeneous pixel set to obtain the target statistically homogeneous pixels of the reference pixels.

[0082] In this embodiment, the spatial consistency test algorithm can be an octree connectivity test algorithm. Specifically, within the gamma distribution confidence interval, the octree connectivity test algorithm is used to identify the statistically homogeneous pixels in the set of connected statistically homogeneous pixels as the target statistically homogeneous pixels for the reference pixels. This embodiment can utilize Monte Carlo simulation and modeling data to verify the effectiveness and accuracy of this method.

[0083] As can be seen from the above, the embodiments of this application determine the reference pixel and the pixel to be detected through a target window, and construct the F-distribution confidence interval of the reference pixel using the F-distribution, thereby filtering the pixel to be detected to obtain candidate pixels. The embodiments of this application also effectively improve the representation ability of local structures and the overall robustness in the reference pixel estimation process by jointly considering the gray-level similarity weight and spatial similarity weight between candidate pixels and reference pixels. Compared with the prior art, the embodiments of this application not only enhance the adaptability to local heterogeneity, but also significantly reduce the estimation bias caused by local noise or structural disturbances. In addition, based on the estimated value of the reference pixel, the embodiments of this application use the gamma distribution confidence interval to filter and obtain a set of statistically homogeneous pixels of the reference pixel, and finally verify the spatial consistency of the pixels in the set of statistically homogeneous pixels based on the spatial consistency test algorithm to obtain the final target statistically homogeneous pixels of the reference pixel. The embodiments of this application further improve the accuracy and effectiveness of homogeneous pixel selection through the above multiple steps.

[0084] In one embodiment, in order to reduce the impact of abnormally high-weight pixels on the estimated value of reference pixels, it is necessary to first correct the joint similarity weights, then normalize the corrected joint similarity weights to obtain the corrected normalized joint similarity weights, and calculate the estimated value of reference pixels based on the corrected normalized joint similarity weights.

[0085] In one embodiment, a weight threshold is calculated based on the joint similarity weight, median, and median absolute deviation. Candidate pixels in the initial candidate pixel set that are greater than or equal to the weight threshold are removed to obtain a target candidate pixel set. The corrected normalized joint similarity weight is obtained based on the target candidate pixel set.

[0086] In this embodiment, the weight threshold can be calculated based on the following formula:

[0087] .

[0088] Where A is the weight threshold, To combine similarity weights, For the pixel to be detected, This is the initial candidate pixel set, median is the calculated median, and MAD is the calculated absolute deviation of the median.

[0089] After removing candidate pixels that are greater than or equal to the weight threshold, the corrected normalized joint similarity weight is constructed, as shown in the following formula:

[0090] .

[0091] The estimated value of the reference pixel can be calculated based on the modified normalized joint similarity weights, using the following formula:

[0092] .

[0093] in, Reference pixel The estimated value, For the corrected normalized weights, For the pixel to be detected The average intensity of the time series.

[0094] This embodiment introduces the concept of a weight threshold, discarding pixels that are greater than or equal to the weight threshold, thus obtaining a final reference pixel. The estimated values ​​are more accurate, which is beneficial for the extraction of homogeneous pixels.

[0095] refer to Figures 2-9 This embodiment uses 31 time-series SAR intensity images (such as...) Figure 2 Taking the example shown below, we will perform statistical homogeneous pixel selection. The specific implementation process includes the following steps:

[0096] Step 1: Acquire 31 original SAR images, perform image registration and interferometry processing to obtain 31 processed time-series SAR intensity images.

[0097] Step 2: Based on the first window (7×7), determine the reference pixel p and the set of pixels to be detected containing multiple pixels to be detected q. The time-series average intensities of the reference pixel and the pixel to be detected under the first window are calculated respectively. The F-distribution confidence interval of the reference pixel is constructed using the F-distribution to obtain the preliminary candidate pixel set for the reference pixel. .

[0098] Step 3, based on the preliminary candidate pixel set The process involves calculating the gray-level Euclidean distance between the candidate pixel and the reference pixel p over time, constructing gray-level similarity weights based on the Gaussian kernel function and the gray-level Euclidean distance; calculating the spatial Euclidean distance between the candidate pixel and the reference pixel p in terms of spatial location, constructing spatial similarity weights based on the spatial decay function and the spatial Euclidean distance; fusing the gray-level similarity weights and the spatial similarity weights to obtain a joint similarity weight, and determining the estimated value of the time-series average intensity of the reference pixel p based on the joint similarity weight. .

[0099] Step 4: Set up a second window (15×15). The pixel located at the center of the second window is the reference pixel p determined under the first window. Use the estimated value of the obtained reference pixel p. Construct a gamma distribution information interval. Pixels within the gamma distribution information interval are defined as a set of statistically homogeneous pixels with the reference pixel p.

[0100] Step 5: Apply the octree connectivity test algorithm to check the spatial consistency of all homogeneous pixels in the statistical homogeneous pixel set of reference pixel p, filter out the final statistical homogeneous pixels (target statistical notification pixels) of reference pixel p, and evaluate and verify them.

[0101] The calculation methods and formulas involved in the above steps can be found in the previous embodiment of this article, and will not be repeated here.

[0102] refer to Figure 3 , Figure 3 This is a schematic diagram illustrating the statistical analysis of homogeneous pixels for a reference pixel p according to an embodiment of this application. p is marked as the position of the reference pixel. The first window is the initial fixed window, with a window size of 7×7. The preliminary candidate pixel set for the reference pixel p obtained through F-segmentation signal interval filtering includes... Figure 3 The image shows light blue and light green pixel blocks, where the light green pixel blocks are SHPs excluded from the reference pixel p based on the corrected joint similarity weights. The second window is a large window corresponding to the reference pixel P, with a window size of 15×15. The connected statistically homogeneous target pixels within the second window are obtained using the gamma distribution confidence interval and octree connectivity test algorithm. Figure 3 The middle part is a light purple pixel block. Figure 3 The dark purple pixel blocks in the second window represent the unconnected SHPs obtained using the octree connectivity test algorithm.

[0103] In this embodiment, after obtaining the final statistically homogeneous pixels (target statistical notification pixels) of the reference pixel p, the effectiveness and accuracy of the temporal InSAR statistically homogeneous pixel selection method proposed in this application embodiment can be verified using Monte Carlo simulation and simulation data. Specifically, the homogeneous pixel selection method proposed in this application embodiment can be evaluated against four commonly used traditional methods (GLRT, KS, BWS, and HTCI) using simulation data and Monte Carlo simulation. Among them, GLRT and HTCI are parametric testing methods, while KS and BWS are non-parametric testing methods.

[0104] refer to Figure 4 (WAHTCI is the result of this method, and the same applies below). Figure 4 (a) From bottom to top, the comparison results of statistical homogeneous pixel identification for WAHTCI, HTCI, GLRT, BWS and KS methods, as well as high-noise data and noise-free data; Figure 4 (b) From bottom to top, the results are the comparison of the optimized interferometric phase recovery of the WAHTCI, HTCI, GLRT, BWS and KS methods, as well as the results of high-noise data and noise-free data. Figure 4 (c) From bottom to top, the comparison results of posterior coherence of WAHTCI, HTCI, GLRT, BWS and KS methods, as well as high-noise data and noise-free data.

[0105] from Figure 4 As can be seen from part (a), in terms of statistical homogeneous pixel recognition performance, the homogeneous pixel regions extracted by the KS, BWS, and GLRT methods exhibit numerous "abrupt changes" or discontinuous boundaries, resulting in patchy, irregular distributions that fail to reflect the structural consistency of real ground features. In contrast, the homogeneous pixel regions identified by the HTCI and WAHTCI methods are more regular and continuously distributed, demonstrating better smoothness and spatial consistency, indicating stronger robustness and stability in high-noise environments. Although the above methods have limitations in interferometric phase optimization (see reference...) Figure 4 (part (b)) and posterior coherence enhancement (refer to) Figure 4The results in part (c) show relatively small differences, all effectively recovering phase information in high-noise regions and significantly improving coherence. However, further quantitative analysis reveals subtle differences in accuracy among the methods. Table 1 lists the mean absolute error between the optimized interferometric phase and the true phase for different statistical homogeneous pixel methods. The results show that the BWS method is superior to the KS method, and the GLRT method is superior to the KS method but slightly inferior to the BWS method. The HTCI method further improves accuracy, with a mean absolute error of 0.0706 rad, while the WAHTCI method further reduces the error to 0.0704 rad, an improvement of approximately 0.28% compared to the HTCI method. These results fully demonstrate that the WAHTCI method has higher reliability and accuracy in homogeneous pixel identification and interferometric phase optimization.

[0106] Table 1. Mean absolute error between the optimized phase and the true phase for each method

[0107]

[0108] Figure 5 This paper presents the distribution of statistically homogeneous pixels identified by various statistical testing methods (KS, BWS, GLRT, HTCI, and WAHTCI) at the central pixel (210, 381) of 31 time-series SAR intensity images. Each green dot represents a neighboring pixel judged as statistically homogeneous with the central pixel. This pixel was selected as the representative analysis object because it is located in the edge transition region between different gray levels, with a gray intensity at a medium-to-high level, and is adjacent to multiple intensity layer bands, resulting in a complex background and significant spatial non-uniformity. Such regions are typically among the most challenging in statistical discrimination: on the one hand, the gray level difference between the central pixel and some neighboring pixels is small, easily leading to "pseudo-homogeneity"; on the other hand, the blurred boundaries of the region can easily cause "over-discrimination" or "under-discrimination" due to differences in the testing sensitivity of the methods themselves.

[0109] refer to Figure 5In terms of the number of homogeneous pixels identified, the KS method identified 85 pixels, which is too broad and has unclear boundaries, posing a risk of introducing non-homogeneous pixels. The BWS method is extremely conservative, identifying only the central pixel (1 pixel) and failing to effectively expand neighborhood information. GLRT identified 32 pixels, a moderate number but with a relatively scattered spatial distribution. The HTCI method identified 46 pixels, and the selected area showed strong spatial clustering and regular boundaries. WAHTCI further improved to 51 pixels, enhancing regional coherence and controlling the possibility of edge misclassification. Overall, HTCI and WAHTCI have significantly better statistical discrimination capabilities than traditional methods in complex, ambiguous boundary areas. In particular, the WAHTCI method achieves a better balance between the number of pixels identified, spatial consistency, and discrimination robustness, verifying its adaptability and stability advantages in high-noise backgrounds.

[0110] refer to Figure 6 and Figure 7 , Figure 6 and Figure 7 These represent the mean and standard deviation of the power of different methods provided in an embodiment of this application under multiple parameter ratios. Figure 6 As can be seen from the parameter ratio ( This is represented as the background region, which is distributed in the same way as the reference pixels. As the contrast of the target region (distributed differently from the reference pixels) increases, the average power of the above methods tends to converge. Among the nonparametric tests (KS, BWS) and parametric tests (GLRT, HTCI), the average power of WAHTCI and HTCI is consistently higher than that of KS, BWS, and GLRT, indicating that they have smaller Type II errors (i.e., higher recognition ability) under different distribution assumptions, and therefore superior performance. Figure 7 As can be seen from the parameter ratio With the increase in contrast, the power standard deviations of the above methods tend to stabilize, and the power standard deviation of the WAHTCI method is better than that of other methods overall, indicating that its detection results are more stable, less volatile, and have better robustness.

[0111] In this embodiment, the evaluation and verification experiment uses a 7×7 window and a 15×15 window, for a total of 225 pixels. The center of the reference pixel is (8,8), and the remaining 224 pixels are used as the pixels to be detected. The left 8 columns (120 pixels) are the background area, distributed the same as the reference pixel, while the right 7 columns (105 pixels) are the target area, distributed differently from the reference pixel. (In parameter ratio...) When the significance level is 1, the background and target areas are statistically indistinguishable, meaning all pixels in the 31 time-series SAR intensity images should be considered homogeneous background. Ideally, the test should not reject any pixels, but since the significance level α is set to 0.05, there is still a false rejection probability of about 5%. Therefore, the expected overall rejection rate should be close to 0.05. Figure 8 It can be seen that the mean power of WAHTCI under this condition is closer to the theoretical value of 0.05 than that of HTCI, which is more in line with expectations and reflects its stronger retention ability for homogeneous pixels (i.e., a lower false rejection rate).

[0112] refer to Figure 9 When the parameter ratio is greater than 1, for example =1.6, indicating a significant difference between the background and target regions. Ideally, the method should completely reject all 105 heterogeneous pixels in the target region while minimizing rejection of the 120 pixels in the background region. However, considering the "false rejections" introduced by α=0.05, an estimated 6 pixels in the background region will be falsely rejected. Combined with the requirement to reject all pixels in the target region, the expected total number of rejected pixels is approximately 111, corresponding to a power mean of 111 / 225 ≈ 0.493. From Figure 9 It can be seen that the average efficacy of WAHTCI is at When the value is 1.6, it is closer to the theoretical value of 0.493, indicating that the method can not only reduce false rejections under low contrast, but also detect heterogeneous pixels more fully under high contrast, and its overall performance is better than the original HTCI method.

[0113] As can be seen from the above, the WAHTCI method provided in this application identifies homogeneous regions with clearer boundaries and more continuous spatial distribution, and the average phase error is reduced by approximately 0.28% compared to the traditional HTCI method. The above experimental results fully demonstrate that the WAHTCI method has significant advantages in improving the accuracy of homogeneous pixel selection and enhancing spatial consistency, and is suitable for high-precision DS-InSAR processing tasks under complex terrain conditions.

[0114] A method for selecting homogeneous pixels in temporal InSAR statistics, corresponding to the above embodiment, Figure 10 This is a block diagram of a temporal InSAR statistical homogeneous pixel selection system provided in one embodiment of this application. For ease of explanation, only the parts relevant to the embodiment of this application are shown. References Figure 10 The time-series InSAR statistical homogeneous pixel selection system 20 includes: an acquisition unit 21, a first processing unit 22, a weight calculation unit 23, a second processing unit 24, and a filtering unit 25.

[0115] Among them, the acquisition unit 21 is used to acquire the reference pixels and the set of pixels to be detected of N time-series SAR intensity images based on the target window;

[0116] The first processing unit 22 is used to calculate the time series average intensity of N time series SAR intensity images. Based on the time series average intensity, the F distribution information interval of the reference pixel is constructed using the F distribution to obtain the preliminary candidate pixel set of the reference pixel. The candidate pixels in the preliminary candidate pixel set belong to the pixel set to be detected.

[0117] The weight calculation unit 23 is used to determine the estimated value of the reference pixel based on the preliminary candidate pixel set, using the gray-scale similarity weight between the candidate pixel and the reference pixel and the spatial similarity weight between the candidate pixel and the reference pixel.

[0118] The second processing unit 24 is used to determine the statistically homogeneous set of the preliminary candidate pixel set and the reference pixel set based on the estimated value of the reference pixel and the gamma distribution information interval.

[0119] The filtering unit 25 is used to filter the pixels in the statistically homogeneous pixel set to obtain the target statistically homogeneous pixel of the reference pixel using the spatial consistency test algorithm.

[0120] In one embodiment of this application, the acquisition unit 21 is specifically used for:

[0121] In N time-series SAR intensity images, the pixels located at the center of the target window are identified as reference pixels, and the set of pixels other than the reference pixels that are located within the target window is identified as the set of pixels to be detected.

[0122] In one embodiment of this application, the weight calculation unit 23 is specifically used for:

[0123] Calculate the gray-level Euclidean distance between candidate pixels and reference pixels in the time series, and construct gray-level similarity weights based on the Gaussian kernel function and the gray-level Euclidean distance;

[0124] Calculate the spatial Euclidean distance between the candidate pixel and the reference pixel in terms of spatial location, and construct spatial similarity weights based on the spatial decay function and the spatial Euclidean distance;

[0125] The gray-scale similarity weight and the spatial similarity weight are fused to obtain the joint similarity weight, and the estimated value of the time series average intensity of the reference pixel is determined based on the joint similarity weight.

[0126] In one embodiment of this application, the weight calculation unit 23 is specifically used for:

[0127] Calculate the weight threshold based on the joint similarity weight;

[0128] Candidate pixels larger than the weight threshold in the initial candidate pixel set are removed to obtain the corrected initial candidate pixel set.

[0129] Based on the revised preliminary candidate pixel set, the revised normalized joint similarity weights are obtained, and the estimated value of the time series average intensity of the reference pixel is determined based on the revised normalized joint similarity weights.

[0130] In one embodiment of this application, the weight calculation unit 23 is specifically used for:

[0131] The weight threshold is calculated based on the following formula:

[0132] .

[0133] Where A is the weight threshold, To combine similarity weights, For the pixel to be detected, This is the initial candidate pixel set, median is the calculated median, and MAD is the calculated absolute deviation of the median.

[0134] In one embodiment of this application, the weight calculation unit 23 is specifically used for:

[0135] The gray-level similarity weights are constructed based on the following formula:

[0136] 。

[0137] in, For grayscale similarity weights, This is the mean of the squared gray-level Euclidean distances of all candidate pixels. This is a preliminary candidate pixel set. Let be the square of the gray-level Euclidean distance of all candidate pixels. It is an exponential function with the natural constant e as its base.

[0138] In one embodiment of this application, the weight calculation unit 23 is specifically used for:

[0139] Spatial similarity weights are constructed based on the following formula:

[0140] 。

[0141] in, For spatial similarity weights, Let be the square of the spatial Euclidean distance of all candidate pixels. It is an exponential function with the natural constant e as its base. It is the square of the largest spatial Euclidean distance among all candidate pixels.

[0142] In one embodiment of this application, the weight calculation unit 23 is specifically used for:

[0143] The joint similarity weight is obtained based on the following formula:

[0144] 。

[0145] in, To combine similarity weights, For the pixel to be detected, For grayscale similarity weights, For spatial similarity weights, This is the initial candidate pixel set.

[0146] See Figure 11 , Figure 11 This is a schematic block diagram of an electronic device provided according to an embodiment of this application. Figure 11 The electronic device 300 in this embodiment may include one or more processors 301, one or more input devices 302, one or more output devices 303, and one or more memories 304. The processors 301, input devices 302, output devices 303, and memories 304 communicate with each other via a communication bus 305. The memories 304 store computer programs, including program instructions. The processors 301 execute the program instructions stored in the memories 304. Specifically, the processors 301 are configured to invoke the program instructions to perform the functions of the units in the above-described device embodiments, for example... Figure 10 The functions of the acquisition unit 21, the first processing unit 22, the weight calculation unit 23, the second processing unit 24, and the filtering unit 25 are shown.

[0147] It should be understood that, in the embodiments of this application, the processor 301 may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0148] Input device 302 may include a touchpad, a fingerprint sensor (for collecting the user's fingerprint information and fingerprint orientation information), a microphone, etc., and output device 303 may include a display (LCD, etc.), a speaker, etc.

[0149] The memory 304 may include read-only memory and random access memory, and provides instructions and data to the processor 301. A portion of the memory 304 may also include non-volatile random access memory.

[0150] In specific implementations, the processor 301, input device 302, and output device 303 described in the embodiments of this application can execute the implementation method described in the temporal InSAR statistical homogeneous pixel selection method provided in the embodiments of this application, or they can execute the implementation method of the electronic device described in the embodiments of this application, which will not be repeated here.

[0151] In another embodiment of this application, a computer-readable storage medium is provided. This computer-readable storage medium stores a computer program, which includes program instructions. When executed by a processor, the program instructions implement all or part of the processes in the methods described above. Alternatively, the computer program can instruct related hardware to complete the process. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include any entity or device capable of carrying computer program code, a recording medium, a USB flash drive, a portable hard drive, a magnetic disk, an optical disk, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium, etc.

[0152] The computer-readable storage medium can be an internal storage unit of the electronic device in any of the foregoing embodiments, such as a hard disk or memory of the electronic device. The computer-readable storage medium can also be an external storage device of the electronic device, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the electronic device. Furthermore, the computer-readable storage medium can include both internal and external storage units of the electronic device. The computer-readable storage medium is used to store computer programs and other programs and data required by the electronic device. The computer-readable storage medium can also be used to temporarily store data that has been output or will be output.

[0153] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this application.

[0154] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the electronic devices and units described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0155] In the several embodiments provided in this application, it should be understood that the disclosed electronic devices and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection through some interfaces or units, or it may be an electrical, mechanical, or other form of connection.

[0156] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of this application, depending on actual needs.

[0157] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0158] The above are merely specific embodiments of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in this application, and such modifications or substitutions should all be covered within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for selecting statistically homogeneous pixels in time-series InSAR, characterized in that, include: Based on the target window, obtain the reference pixels and the set of pixels to be detected for N time-series SAR intensity images; Calculate the time series average intensity of the N time series SAR intensity images, and based on the time series average intensity, construct the F-distribution information interval of the reference pixel using the F-distribution to obtain the preliminary candidate pixel set of the reference pixel. The candidate pixels in the preliminary candidate pixel set belong to the pixel set to be detected. Based on the preliminary candidate pixel set, the estimated value of the reference pixel is determined by using the gray-level similarity weight between the candidate pixel and the reference pixel, and the spatial similarity weight between the candidate pixel and the reference pixel. Based on the estimated value of the reference pixel, the statistically homogeneous set of pixels in the preliminary candidate pixel set and the reference pixel is determined using the gamma distribution information interval. The target statistically homogeneous pixels of the reference pixels are obtained by filtering the pixels in the statistically homogeneous pixel set using a spatial consistency test algorithm. Specifically, based on the preliminary candidate pixel set, the estimated value of the reference pixel is determined using the gray-level similarity weight between the candidate pixels and the reference pixel, and the spatial similarity weight between the candidate pixels and the reference pixel, including: Calculate the gray-level Euclidean distance between the candidate pixel and the reference pixel in the time series, and construct gray-level similarity weights based on the Gaussian kernel function and the gray-level Euclidean distance; Calculate the spatial Euclidean distance between the candidate pixel and the reference pixel in terms of their spatial locations, and construct spatial similarity weights based on the spatial decay function and the spatial Euclidean distance; The gray-scale similarity weight and the spatial similarity weight are fused to obtain a joint similarity weight, and the estimated value of the time series average intensity of the reference pixel is determined based on the joint similarity weight.

2. The method of claim 1, wherein, The method for acquiring the reference pixel and the set of pixels to be detected for N time-series SAR intensity images based on the target window includes: In N time-series SAR intensity images, the pixels located at the center of the target window are determined as reference pixels, and the set of pixels other than the reference pixels that are located within the target window is taken as the set of pixels to be detected.

3. The method of claim 1, wherein, The step of determining the estimated time-series average intensity of the reference pixel based on the joint similarity weight includes: Calculate the weight threshold based on the joint similarity weight; Candidate pixels in the initial candidate pixel set that are greater than the weight threshold are removed to obtain a corrected initial candidate pixel set. Based on the corrected preliminary candidate pixel set, the corrected normalized joint similarity weights are obtained, and the estimated value of the time series average intensity of the reference pixel is determined based on the corrected normalized joint similarity weights.

4. The method of claim 3, wherein, The calculation of the weight threshold based on the joint similarity weight includes: The weight threshold is calculated based on the following formula: A Where A is the weight threshold, To combine similarity weights, For the pixel to be detected, This is the initial candidate pixel set, median is the calculated median, and MAD is the calculated absolute deviation of the median.

5. The method of claim 1, wherein, The construction of gray-level similarity weights based on the Gaussian kernel function and the gray-level Euclidean distance includes: The gray-level similarity weights are constructed based on the following formula: in, For grayscale similarity weights, This is the mean of the squared gray-level Euclidean distances of all candidate pixels. This is a preliminary candidate pixel set. Let be the square of the gray-level Euclidean distance of all candidate pixels. It is an exponential function with the natural constant e as its base.

6. The method of claim 1, wherein, The construction of spatial similarity weights based on the spatial decay function and the spatial Euclidean distance includes: Spatial similarity weights are constructed based on the following formula: wherein, is a spatial similarity weight, is the square of the spatial Euclidean distance of all candidate pixels, is an exponential function with base e, is the square of the maximum spatial Euclidean distance of all candidate pixels.

7. The method of claim 1, wherein, The step of fusing the grayscale similarity weight and the spatial similarity weight to obtain a joint similarity weight includes: The joint similarity weight is obtained based on the following formula: in, To combine similarity weights, For the pixel to be detected, For grayscale similarity weights, For spatial similarity weights, This is the initial candidate pixel set. 8.A system for selecting statistically homogeneous pixels in time-series InSAR, characterized in that, include: The acquisition unit is used to acquire reference pixels and a set of pixels to be detected for N time-series SAR intensity images based on the target window; The first processing unit is used to calculate the time series average intensity of the N time series SAR intensity images, and based on the time series average intensity, construct the F distribution information interval of the reference pixel using the F distribution to obtain the preliminary candidate pixel set of the reference pixel. The candidate pixels in the preliminary candidate pixel set belong to the pixel set to be detected. The weight calculation unit is used to determine the estimated value of the reference pixel based on the preliminary candidate pixel set, using the gray-level similarity weight between the candidate pixel and the reference pixel and the spatial similarity weight between the candidate pixel and the reference pixel; The weight calculation unit is specifically used to calculate the gray-level Euclidean distance between the candidate pixel and the reference pixel in the time series, and to construct gray-level similarity weights based on the Gaussian kernel function and the gray-level Euclidean distance. Calculate the spatial Euclidean distance between the candidate pixel and the reference pixel in terms of their spatial locations, and construct spatial similarity weights based on the spatial decay function and the spatial Euclidean distance; The gray-scale similarity weight and the spatial similarity weight are fused to obtain a joint similarity weight, and the estimated value of the time series average intensity of the reference pixel is determined based on the joint similarity weight. The second processing unit is used to determine the set of statistically homogeneous pixels in the preliminary candidate pixel set and the reference pixel using gamma distribution information intervals based on the estimated value of the reference pixel. The filtering unit is used to filter the pixels in the statistically homogeneous pixel set using a spatial consistency test algorithm to obtain the target statistically homogeneous pixel of the reference pixel.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1 to 7.

Images