SAR image mountain shadow dynamic threshold removing method based on inverse exponential function

Abstract

The invention discloses an SAR image mountain shadow dynamic threshold removal method based on an inverse exponential function, and relates to the technical field of remote sensing image data processing, and the method comprises the steps: preliminarily extracting a water body region based on an SAR image through employing a dual polarization water body index SDWI, and randomly generating sample points in the range of the water body region; assigning corresponding elevation and gradient attributes to each sample point through digital elevation data SRTM, and performing artificial interpretation by using an optical image to obtain a sample data set containing two types of sample points of a mountain shadow and a water body; and removing abnormal values of a sample data set through a quartile distance method, performing thinning processing on sample points to calculate a demarcation point of the two types of sample points, and constructing a demarcation function model of an inverse index for distinguishing a mountain shadow and a water body. Therefore, by adopting the SAR image mountain shadow dynamic threshold removal method based on the inverse exponential function, the false water body region caused by the misjudgment of the terrain shadow is effectively eliminated, and the authenticity and the consistency of the water body space distribution are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of remote sensing image data processing, and in particular to a method for removing dynamic thresholds of mountain shadows in SAR images based on an inverse exponential function. Background Technique

[0002] With the development of remote sensing technology, synthetic aperture radar (SAR), with its all-weather and all-day acquisition capabilities, has become one of the mainstream data sources for dynamic monitoring of flood disasters. However, during the process of flood water body extraction, the interference problem of mountain shadows in SAR images has become increasingly prominent and has become a key bottleneck affecting the accuracy and automation of flood extraction.

[0003] The imaging method of SAR images determines their high sensitivity to the backscattering intensity of ground objects. When radar waves are incident on high-relief terrains (such as mountains), shadow areas are easily formed. These areas have extremely low gray values due to the lack of backscattering signals and have image characteristics highly similar to actual water pixels, namely the so-called "spectral similarity of different objects" phenomenon. This phenomenon can easily lead to misclassification during image interpretation and automated water body recognition, seriously affecting the accuracy and reliability of flood extraction.

[0004] To address this problem, the following methods are mainly used in the academic and engineering practices to remove mountain shadows. Machine learning is a popular method for flood detection in recent years. Inspired by convolutional neural networks (CNNs), various CNN-based detection methods have emerged, including DASNet, DTCDSCN, Siam-NestedUNet, AFDE-Net, and SNUNet-CD. Although machine learning methods have great potential in flood detection, convolutional neural networks (CNNs) have a limited receptive field and are difficult to accurately distinguish water bodies from interfering objects, reducing the performance of the models used for flood detection. In contrast, in the preprocessing or postprocessing stages of flood detection tasks, methods that use auxiliary information provided by terrain data such as digital elevation models (DEMs) to remove mountain shadows have been more widely applied. Common methods include the formation mechanism method, the HAND (Height Above Nearest Drainage) model, and the slope threshold method, etc.

[0005] Among them, the formation mechanism method simulates the mountain shadow area based on the imaging geometric parameters of SAR radar images (such as satellite orbit azimuth angle, incident angle, etc.) and DEM data, and removes it accordingly. Although this method starts from the imaging principle and has certain theoretical advantages, due to the need to accurately obtain radar imaging parameters and perform mathematical modeling, its processing flow is relatively complex and the application difficulty is relatively high.

[0006] The HAND method calculates the relative terrain height using DEM data. When the HAND threshold is reasonably set, it can effectively mask non-water areas. In addition, some studies have attempted to optimize the removal of mountain shadows using digital surface model (DSM) data. For example, the method combining topological separation and local DSM search can effectively eliminate most misclassified areas, but there are still jagged noises at the boundaries of some water areas.

[0007] The slope threshold method has been widely used in the removal of mountain shadows due to its simplicity and high efficiency. This method calculates the slope based on DEM and sets a slope threshold to distinguish mountain shadow areas. However, the slope threshold method has the problems of relying on manual threshold setting by users, being highly subjective and experience-dependent. The setting of a fixed threshold lacks terrain adaptability and is not conducive to the stable migration and automated processing of the model.

[0008] In summary, the existing methods for removing mountain shadows from SAR images have limitations to varying degrees in terms of theoretical models, processing flows, and practical applicability. The formation mechanism method is highly theoretical but cumbersome to operate. The HAND method is computationally convenient but has single information. The slope method is efficient but the threshold is not self-adaptive. It is difficult for all three methods to achieve the unity of accuracy, adaptability, and simplicity of operation under different scales and terrain backgrounds. Summary of the Invention

[0009] The purpose of the present invention is to provide a method for dynamically removing mountain shadows from SAR images based on an inverse exponential function to solve the misclassification problem caused by the "same spectrum of foreign objects" of mountain shadows in the existing SAR image water extraction, especially the problems of poor adaptability and high mis-removal rate of the fixed slope threshold method in complex terrain areas.

[0010] To achieve the above purpose, the present invention provides a method for dynamically removing mountain shadows from SAR images based on an inverse exponential function, including the following steps: S1. Obtain the SAR image, digital elevation data, and optical image at the corresponding time, preprocess the obtained data to unify the spatial resolution and project it onto the same spatial coordinate system; S2. Based on the SAR image, use the dual-polarization water index or fixed threshold segmentation to preliminarily extract the water area, calculate the elevation and slope of each pixel point using the digital elevation data, randomly generate sample points within the preliminarily extracted water area, assign the corresponding elevation and slope attributes to the sample points, and then obtain the sample data set through manual interpretation of the optical image; the sample data set contains two types of samples: mountain shadows and water; S3. Remove the outliers in the sample data set by the interquartile range method, thin the sample points, calculate the demarcation point of the two types of sample points in the spatial rectangular coordinate system, construct the demarcation function model of the inverse exponential, and then use this demarcation function model to distinguish mountain shadows and water.

[0011] Preferably, in step S3, the first quartile Q1 of the interquartile range method is set to 10%, and the third quartile Q3 is set to 90% to maintain the true distributions of the two types of samples, namely mountain shadows and water bodies.

[0012] Preferably, in S3, calculating the boundary point between the two types of sample points includes calculating all the distances between the two types of sample points, selecting several groups of sample points with small distances, and taking the midpoint of the distances as the boundary point to determine the boundary function model.

[0013] Preferably, when calculating the boundary point between the two types of sample points in S3, first convert the sample points from the elevation-slope coordinate system to the plane rectangular coordinate system, then calculate the Euclidean distances between the two types of sample points to obtain the corresponding boundary point, and then convert it back to the elevation-slope coordinate system. Introduce an inverse exponential curve to construct the boundary function model.

[0014] Preferably, the boundary function model of the inverse exponential in S4 has the following expression: ; In the formula, and are the parameters of the boundary function model, represents elevation, represents slope.

[0015] Preferably, constructing the boundary function model of the inverse exponential includes using the grid search method to optimize the parameters of the boundary function model and , as follows: First, according to the boundary point, determine the intervals of the parameters and through local grid search, and linearly divide the intervals of each parameter to generate candidate parameter values; Then, use global grid search to traverse each group of candidate parameter values, and apply the classification rules of the boundary function model to distinguish mountain shadows and water bodies; After that, evaluate the classification performance of this group of candidate parameter values by calculating the accuracy between the classification result and the true label, and obtain the optimized parameter and values, so as to determine the boundary function model.

[0016] Therefore, the present invention adopts the above-mentioned method for removing the dynamic threshold of mountain shadows in SAR images based on the inverse exponential function, and has the following technical effects: (1) The present invention automatically determines the optimal parameter combination through grid search, constructs an inverted exponential boundary function model without the need for manual setting of fixed thresholds, significantly reducing the dependence on the experience of users; at the same time, the inverted exponential boundary function model supports rapid deployment and large-scale automated processing on platforms such as Google Earth Engine (GEE), realizing automation and parameter self-adaptation.

[0017] (2) Compared with the formation mechanism method that requires precise modeling and the HAND method that manually sets parameters, the structure of the present invention is clear, the steps are standardized, without cumbersome geometric simulation and local calculation, with high operating efficiency, capable of achieving rapid operation and stable result output, and is especially suitable for flood disaster monitoring tasks in emergency response scenarios.

[0018] (3) The inverted exponential function proposed by the present invention has the ability of non-linear boundary adjustment, can dynamically adjust the slope discrimination condition according to different elevations, avoid the phenomenon that real water bodies are mis-eliminated by fixed thresholds in mountainous areas, effectively improve the integrity and reliability of the extraction results, and has strong water body integrity protection ability.

[0019] (4) The present invention can be directly integrated into the flood monitoring and early warning system, providing more timely and accurate remote sensing data support for relevant departments such as government emergency management, meteorology, water conservancy, and ecology; in the event of sudden flood disasters, it can achieve efficient and automated extraction of flooded areas, providing a decision-making basis for emergency dispatch and personnel evacuation, and has broad application prospects and disaster reduction value.

[0020] The technical solution of the present invention will be further described in detail below through the accompanying drawings and embodiments. Description of the Drawings

[0021] Figure 1 is a flowchart of the method for dynamically removing mountain shadows in SAR images based on the inverted exponential function; Figure 2 is a schematic diagram of calculating the boundary midpoint of downsampled sample points in the embodiment of the method for dynamically removing mountain shadows in SAR images based on the inverted exponential function; Figure 3 is the inverted exponential boundary function model in the embodiment of the method for dynamically removing mountain shadows in SAR images based on the inverted exponential function; Figure 4 is a schematic diagram of applying the inverted exponential boundary function model to distinguish water body sample points and mountain shadow sample points in the elevation-slope coordinate system in the embodiment of the method for dynamically removing mountain shadows in SAR images based on the inverted exponential function; Figure 5 is the SAR flood extraction map before monitoring mountain shadows in the embodiment of the method for dynamically removing mountain shadows in SAR images based on the inverted exponential function; Figure 6 This is the SAR flood extraction map after monitoring mountain shadows in the embodiment of the method for removing dynamic thresholds of mountain shadows in SAR images based on the inverse exponential function. Among them, black represents mountain shadows, and red represents floods; Figure 7 This is the comparative analysis result of different models in the embodiment of the method for removing dynamic thresholds of mountain shadows in SAR images based on the inverse exponential function. Among them, (a) is the optical image, (b) is the method of the present invention, (c) is the HAND method, and (d) is the formation mechanism method. Detailed implementation manners

[0022] The present invention can be more detailedly explained through the following embodiments. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following embodiments.

[0023] Embodiment 1 Since the existing methods for removing mountain shadows have limitations: (1) The formation mechanism method is computationally complex and highly parameter-dependent, making it difficult to be efficiently deployed; (2) The HAND method only considers elevation information and is prone to misdeleting water bodies; (3) Although the slope threshold method is efficient, the fixed threshold does not have self-adaptive ability and performs unstably under different geomorphic conditions, easily reducing the extraction accuracy.

[0024] Aiming at the problems existing in the prior art, the present invention provides a method for removing dynamic thresholds of mountain shadows in SAR images based on the inverse exponential function, aiming to build an elevation-slope feature space, introduce the inverse exponential function to establish a classification boundary, realize the dynamic adjustment of the slope threshold and terrain self-adaptive division, so as to improve the accuracy and automation of removing mountain shadows in SAR flood monitoring, and is applicable to the rapid flood extraction task of large-scale complex terrains. Please refer to Figure 1 .

[0025] In this embodiment, three types of data are mainly used: Sentinel-1 SAR images, digital elevation data SRTM, and Sentinel-2 optical images. The core idea is to build an "elevation-slope" feature space, introduce the inverse exponential function as a dynamic classification boundary function, and combine the grid search algorithm to select the optimal parameters to build a boundary function for water bodies / mountain shadows.

[0026] Whether the boundary function can accurately remove mountain shadows depends on the construction of the sample data set. The goal of this stage is to extract the flood water body area and build geographical sample points with elevation-slope feature information to provide a data basis for model training.

[0027] In the first stage, the water body area is extracted.

[0028] In this embodiment, Sentinel-1 SAR images are retrieved through the Google Earth Engine (GEE) platform. The polarization modes are VV and VH, the spatial resolution is 10 m, and the acquisition time of the images is August 5, 2023, during which a flood disaster occurred. Among them, the Sentinel-1 SAR images retrieved by GEE have undergone preprocessing such as thermal noise removal, radiometric calibration, and terrain correction, and users do not need to manually perform these data preprocessing steps.

[0029] Based on the Sentinel-1 SAR image data, the Sentinel-1 Dual-Polarized Water Index (SDWI) is used for water body extraction. This index is used to calculate the difference between Sentinel-1 dual-polarized (VV and VH) data, enhancing the water body features. The calculation formula of the SDWI index is as follows: ; In the formula, VH and VV are Sentinel-1 dual-polarized backscatter data; SDWI is the result value of the band mathematical operation. Pixels with a calculated result greater than 0 are determined as water bodies, obtaining a water body / non-water body binary map.

[0030] In other embodiments, the water body area can be preliminarily extracted by the method of fixed thresholds in the prior art.

[0031] The second stage is to construct a sample data set.

[0032] In this embodiment, Digital Elevation Model (DEM) data is retrieved through the GEE platform, which is from the SRTM data set with a spatial resolution of 30 m. To ensure the spatial matching of data with different spatial resolutions, in this embodiment, the DEM data with a 30 m spatial resolution is resampled to 10 m, and all data is uniformly converted to the GCS_WGS_1984 projection.

[0033] Based on the SRTM data set, the elevation and slope information of each pixel point in the study area is calculated. According to the area of the study area and a reasonable sample density, 7000 random sample points are generated within the SDWI water body mask range in this embodiment, and elevation and slope attributes are assigned to all sample points. Then, using the Arcmap software, the Sentinel-2 optical images of the same period (the shooting date is August 15) are used for auxiliary interpretation, and the true category (mountain shadow or water body) of each sample point is manually visually labeled, finally constructing a sample set with two-dimensional feature (elevation, slope) classification labels, among which there are about 1737 water body points and 5263 mountain shadow points.

[0034] Due to the measurement accuracy problem and spatial resolution problem of SRTM data, the calculation of slope will be affected, which will lead to the appearance of abnormal points. However, most of the abnormal values are due to human visual misjudgment. Data measurement errors and visual interpretation errors often have randomness, which will cause the distribution of data to deviate from the normal distribution. To solve this problem, this embodiment uses the Inter - quartile Range (IQR) method to remove the abnormal values in the scatter plot. This method is simple to operate, easy to implement, and has strong robustness and is not easily affected by extreme values in the data set. Since the water body sample points are mainly concentrated in the lower elevation and slope areas, while the shadow sample points are widely distributed and show a skewed distribution, the traditional IQR method will misjudge a large number of normal data points as outliers. Therefore, in this embodiment, the first quartile Q1 is set to 10% (0.1), and Q3 is set to 90% (0.9), which not only removes some abnormal values but also maintains the integrity of the sample points, retains enough sample points to represent their respective true distributions, and a total of 42 sample points are removed, including 11 water body sample points and 31 mountain shadow sample points.

[0035] To better fit the classification boundary, this embodiment determines the parameter value range of the inverse exponential function by calculating the midpoint of the two types of sample points. After removing the outliers, the number of sample points is still huge, and it is difficult to directly calculate the boundary midpoint of all sample points. Therefore, it is necessary to thin out the sample points. This embodiment also needs to convert the elevation - slope coordinate system into a plane rectangular coordinate system because the midpoint calculated using the distance formula in the elevation - slope coordinate system cannot reflect the classification boundary of the two types of sample points. Therefore, on the premise of keeping the spatial position of the sample points consistent, it is converted into a plane rectangular coordinate system for mathematical operations. Specifically: (1) Calculate the coordinate range of the water body point data, and then take into account the coordinate range of the shadow point data to finally obtain a global coordinate range that can contain all data points. The purpose of doing this is to ensure that in subsequent coordinate conversions, all data points can be correctly mapped to the new coordinate system to avoid data loss.

[0036] (2) Define a linear mapping function that maps any value in the original coordinate range to the new target range. This mapping is order - preserving, that is, the relative position relationship between the original data points is retained in the new coordinate system. The mathematical principle is to achieve value range conversion through proportional scaling and translation.

[0037] (3) Use the matplotlib library to create a scatter plot and visually display the converted water body points and shadow points in the new Cartesian coordinate system. Figure 2 The blue points represent the water body, and the orange points represent the mountain shadow. The horizontal and vertical coordinate ranges are both from 0 to 5, forming a standard first - quadrant plane rectangular coordinate system.

[0038] Then, in the new coordinate system, new coordinate values are re-assigned to the sample points, and all distances between the two types of sample points are calculated using the Euclidean distance formula. To ensure that the boundary points can represent most classification situations and at the same time reduce the computational amount, please refer to Figure 2 , in this embodiment, six groups of sample points with the smallest distances are selected, and the midpoints of the distances between the two types of sample points are calculated as the demarcation points between the two types of samples, which are used to construct the demarcation function model and provide the initial conditions for function fitting to ensure that the demarcation function accurately demarcates the mountain shadow and water body areas. This method is of key significance in model construction. On the one hand, through coordinate system transformation and distance discrimination, representative boundary points can be accurately extracted in the feature space, avoiding the increase in computational complexity caused by sample redundancy; on the other hand, the acquisition of the classification midpoint provides a stable and reasonable boundary reference for the initial fitting of the inverse exponential function, which helps to improve the fitting degree of the function curve to the real classification boundary.

[0039] Existing technologies generally use linear functions as thresholds to distinguish mountain shadows and water bodies, but this method lacks terrain adaptability and is not conducive to the stable migration and automated processing of the model. To solve this problem, this embodiment uses an inverse exponential function as the demarcation function model. The morphological characteristics of this function can more accurately fit the boundary of water body and mountain shadow sample points, thereby improving the classification accuracy. Please refer to Figure 3 .

[0040] In the elevation and slope coordinate system (please refer to Figure 4 ), the parameters in the inverse exponential function and have clear physical meanings. The magnitude of its parameter determines the final horizontal position of the function curve, that is, when the elevation approaches infinity, the value of the slope will gradually approach . This characteristic can effectively simulate the disappearance phenomenon of mountain shadows in the low-slope area. In existing methods, the parameter is also used as a fixed threshold to eliminate mountain shadows, that is, the pixels exceeding this threshold are identified as shadow noise and eliminated. Especially in areas with high elevation but low slope, such as river areas in mountainous areas, the parameter can prevent these areas from being misjudged as mountain shadows.

[0041] The parameter controls the attenuation rate of the function. A larger value will cause the function to decay rapidly when the value is small. Since the value range of the slope does not exceed 90°, and the elevation The value will not be lower than a certain specific value, that is, there is an elevation threshold for mountain shadows in the inverse exponential function model. Mountain shadows below this elevation threshold will not be misjudged as water bodies. This also conforms to the characteristic that there are no mountain shadows in low-elevation areas such as plains.

[0042] Compared with the linear function, the concave curve shape presented by the inverse exponential function provides stronger fitting ability. Especially when dealing with complex terrain data, this non-linear curve can more accurately describe the boundary between water bodies and mountain shadows.

[0043] Then, the coordinate system is converted back to the elevation-slope coordinate system, and the thinned sample points are restored to prepare for optimizing the parameters and , and better distinguish the two types of sample points with the inverse exponential function.

[0044] When optimizing the parameters and , this embodiment adopts the grid search method to discretize the parameters of the model and conduct an exhaustive search one by one on the pre-set parameter grid to find the optimal parameter combination, which is specifically divided into two parts: The first part is to set the parameter search interval. The interval of parameter is set to [4, 6], and the interval of parameter is set to [150, 180]. The selection of the interval is not arbitrary, but based on the calculated breakpoint values, the shape of the inverse exponential function curve is fitted to determine the upper and lower limits of the values of parameters and , and then the obtained interval values are rounded down to determine the above search interval, specifically as follows: First, based on the calculated 6-component midpoints, each midpoint is used as the representative point for demarcation, and a local grid search model is constructed using the demarcation function model of the inverse exponential. In the local grid search, by systematically adjusting the parameters and within the set parameter candidate set, with the maximization of the classification accuracy as the optimization goal, determine the local optimal parameter combination that can optimally divide the water body and the mountain shadow by the demarcation function model of the inverse exponential. Taking the first midpoint as an example, fix the midpoint coordinates, and find the parameters and that can accurately classify this point and have the highest classification accuracy in its local neighborhood through grid search. According to this method, the same local grid search is carried out for the remaining 5 groups of midpoints respectively, and finally 6 groups of local optimal parameter results are obtained.

[0045] Then, perform statistical analysis on the 6 groups of locally optimal parameters, and extract the minimum and maximum values of parameters a and b. In order to retain sufficient search space to avoid underfitting, in this embodiment, the truncation method is used to round the boundary values, and the search interval of the model parameters is determined as and . In this part, local grid search uses the midpoint of the boundary to quickly narrow the parameter search space and improve the optimization efficiency.

[0046] In the second part, after determining the parameter search interval, based on all sample data, continue to use the grid search method within the above interval, and finally obtain the overall optimal parameter combination of the model by maximizing the objective function of the overall classification accuracy, as follows: First, perform a linear division between the intervals [4, 6] and [150, 180] to generate a series of candidate parameter values. Traverse each candidate parameter pair and apply the classification rule, that is, when the slope value Slope of the sample is greater than the function value , it is classified as mountain shadow (label 1), otherwise it is classified as water body (label 0).

[0047] Then, for each parameter combination, calculate the accuracy between the classification result and the true label to evaluate the classification performance of this combination. Finally, select the parameter combination that can maximize the accuracy as the optimal parameter of the model, and obtain the optimal values of parameters and .

[0048] Through the grid search strategy in the above two parts, the parameter space is effectively reduced with local midpoint samples, improving the computational efficiency of model optimization. At the same time, through the global optimization of all samples, the classification accuracy of the model and its applicability under complex terrain conditions are guaranteed.

[0049] After multiple parameter optimizations and model adjustments, the model finally achieved the best accuracy of 0.98 on the test data set, correctly identifying 1737 water body pixels and 5263 mountain shadow pixels, with only a small number of misclassified pixels. The misclassified samples include 35 mountain shadow pixels misjudged as water bodies and 105 water body pixels misjudged as mountain shadows. The Kappa coefficient is 0.95, and the overall accuracy reaches 98%. The optimal parameters determined by the network search method in this embodiment are , , then the optimal model is: .

[0050] The high accuracy of the model largely benefits from the good match between the mathematical model of the inverse exponential function and the data feature distribution. After removing sample outliers, the feature differences between samples are more significant, making the classification boundary clearer, and the inverse exponential function model can also divide samples more accurately. In addition, and The two parameters reached the optimal values. The optimization of the parameters enabled the inverse exponential function model to better adapt to the data characteristics during the training process, thereby improving the classification effect.

[0051] In the model application, first, the SDWI (Water Body Bipolarization Index) is used to enhance the water body features, and a suitable threshold is set for binary processing to extract the flood inundation area. Please refer to Figure 5 . It can be seen that before the mountain shadows were monitored, there were a large number of misjudged "false water bodies" in the mountainous area in the northwest of the study area. These areas were shown as patchy water body distributions in the figure that were inconsistent with the actual water body morphology. To distinguish real water bodies from mountain shadows, in this embodiment, the SRTM digital elevation model (DEM) data is retrieved, and the corresponding elevation and slope information is assigned to each pixel in the flood extraction result, and the elevation and slope values are associated with each water body pixel to form a water body candidate data set containing elevation-slope spatial features. Then, the elevation value of each pixel in the image water body area is brought into this function. If the slope value (Slope) of this pixel point is greater than the function value , it is determined as a mountain shadow and classified into the non-water body area. By this method, during the process of extracting water bodies from SAR images, the interference of mountain shadows on the results is eliminated. Please refer to Figure 6 . In other embodiments, the model obtained by the present invention can be directly migrated to remote sensing image processing software such as ENVI and Arcmap for application.

[0052] Embodiment 2 To verify the effect of the boundary function model of the inverse exponential in the present invention in eliminating mountain shadows, in this embodiment, two widely used and highly representative methods are selected for comparative analysis: the formation mechanism method and the relative height of the nearest neighbor river channel HAND method.

[0053] Please refer to Figure 7 . Taking the reservoir in the mountainous area as an example, the formation mechanism method has a poor effect, leaving more mountain shadows and wrongly deleting water bodies; in addition, this method has a large amount of calculation and a complex processing process, and is not suitable for rapid response, especially in application scenarios such as flood disasters that require real-time data processing. Although HAND is simple to operate, it will also wrongly delete water bodies (such as the northeast corner of the reservoir). This is because this method only considers the elevation feature, resulting in the easy identification of water bodies as non-water bodies at the edge of mountainous water bodies, affecting the integrity of water bodies; in addition, the HAND method requires pre-setting a threshold, and this process depends on empirical judgment, resulting in inaccurate selection of the threshold, further affecting the integrity and accuracy of water bodies.

[0054] In contrast, the present embodiment adopts an inverse exponential boundary function model, which can comprehensively consider the dual characteristics of elevation and slope. Based on the fixed slope threshold method, it is improved to adaptively adjust the threshold according to the terrain features, thereby improving the adaptability and accuracy of the model in complex terrains and avoiding the errors and omissions caused by the setting of fixed thresholds. At the same time, the application process of the inverse exponential boundary function model is simple and efficient, greatly reducing the user participation and complexity and the dependence on empirical judgment.

[0055] Therefore, by adopting the above SAR image mountain shadow dynamic threshold removal method based on the inverse exponential function, the present invention can effectively exclude the false water body areas misjudged due to terrain shadows before, improving the authenticity and consistency of the water body spatial distribution, and the effect is more obvious especially in complex terrains such as mountainous areas and piedmont plains.

[0056] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for removing the dynamic threshold of mountain shadows in SAR images based on the inverse exponential function, characterized in that Including the following steps: S1. Obtain SAR images, digital elevation data, and optical images at the corresponding time, preprocess the obtained data to unify the spatial resolution, and project them onto the same spatial coordinate system; S2. Based on the SAR images, use the dual-polarization water index or fixed threshold segmentation to preliminarily extract the water area, calculate the elevation and slope of each pixel point using the digital elevation data, randomly generate sample points within the preliminarily extracted water area, assign the corresponding elevation and slope attributes to the sample points, and then obtain the sample data set through manual interpretation of the optical images; the sample data set contains two types of samples: mountain shadows and water bodies; S3. Remove the outliers in the sample data set by the interquartile range method, thin out the sample points, calculate the demarcation point between the two types of sample points in the space rectangular coordinate system, construct the demarcation function model of the inverted exponential, and then use this demarcation function model to distinguish mountain shadows and water bodies.

2. The method for removing the mountain shadow dynamic threshold of SAR images based on the inverse exponential function according to claim 1, wherein In S3, the first quartile Q1 of the interquartile range method is set to 10%, and the third quartile Q3 is set to 90% to maintain the true distributions of the two types of samples of mountain shadows and water bodies respectively.

3. The method for removing the mountain shadow dynamic threshold of SAR images based on the inverse exponential function according to claim 1, wherein Calculating the demarcation point between the two types of sample points in S3 includes calculating all the distances between the two types of sample points, selecting several groups of sample points with small distances, and taking the midpoint of the distances as the demarcation point to determine the parameters of the demarcation function model.

4. The method for removing the mountain shadow dynamic threshold of SAR images based on the inverse exponential function according to claim 3, characterized in that, When calculating the demarcation point between the two types of sample points in S3, first convert the sample points from the elevation-slope coordinate system to the plane rectangular coordinate system, then calculate the Euclidean distances between the two types of sample points to obtain the corresponding demarcation points, and then convert them back to the elevation-slope coordinate system, introduce the inverted exponential curve, and construct the demarcation function model.

5. The method for removing the mountain shadow dynamic threshold of SAR images based on the inverse exponential function according to claim 1, characterized in that The demarcation function model of the inverted exponential in S4 has the following expression: ； In the formula, , are the parameters of the boundary function model, represents the elevation, represents the slope.

6. The method for removing the mountain shadow dynamic threshold of SAR images based on the inverse exponential function according to claim 5, wherein Building the boundary function model of the inverse exponential includes using the grid search method to optimize the parameters of the boundary function model and , as follows: First, according to the demarcation point, determine the intervals of parameters and through local grid search, and linearly divide the intervals of each parameter to generate candidate parameter values; Then, use the global grid search to traverse each set of candidate parameter values, and apply the classification rules of the demarcation function model to distinguish mountain shadows and water bodies; After that, by calculating the accuracy between the classification result and the true label, the classification performance of this group of candidate parameter values is evaluated, and the optimized parameters and values are obtained to determine the boundary function model.

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