Dynamic threshold removal method of hill shadow in SAR images based on inverse exponential function

Abstract

The present invention discloses a method for removing mountain shadows from SAR images using a dynamic threshold based on an inverse exponential function, which relates to the technical field of remote sensing image data processing. The method comprises the following steps: preliminarily extracting water areas based on SAR images using the dual-polarization water index (SDWI), and randomly generating sample points within the water area; assigning corresponding elevation and slope attributes to each sample point using digital elevation data (SRTM), and then manually interpreting the optical image to obtain a sample data set containing two types of sample points: mountain shadows and water bodies; removing outliers from the sample data set using the interquartile range method, performing a thinning process on the sample points to calculate the dividing point between the two types of sample points, and constructing an inverse exponential dividing function model for distinguishing mountain shadows from water bodies. Therefore, the above-mentioned method for removing mountain shadows from SAR images using a dynamic threshold based on an inverse exponential function effectively eliminates false water areas misjudged due to terrain shadows, thereby improving the authenticity and consistency of the spatial distribution of water bodies.

Description

Technical Field

[0001] The invention relates to the technical field of remote sensing image data processing, in particular to a SAR image mountain shadow dynamic threshold removal method based on an inverse exponential function. Background Art

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

[0003] SAR imagery, due to its imaging method, is highly sensitive to the backscatter intensity of ground objects. When radar waves strike high-elevation terrain (such as mountains), shadow areas are easily formed. These areas, lacking backscatter signals, exhibit extremely low grayscale values, resulting in image characteristics highly similar to those of actual water pixels. This phenomenon, known as the "different objects, same spectrum" phenomenon, can easily lead to misclassification during image interpretation and automated water body identification, severely impacting the accuracy and reliability of flood and waterlogging extraction.

[0004] To address this issue, the following methods are currently used in academia and engineering practice to remove hillshades. Machine learning has become 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 for flood detection, convolutional neural networks (CNNs) have limited receptive fields and difficulty accurately distinguishing water bodies from interfering objects, which reduces the performance of models used for flood detection. In contrast, methods that utilize auxiliary information provided by terrain data such as digital elevation models (DEMs) to remove hillshades have become more widely used in the pre-processing or post-processing stages of flood detection tasks. Common methods include the formation mechanism method, the HAND (Height Above Nearest Drainage) model, and the slope threshold method.

[0005] The formation mechanism method simulates mountain shadow areas based on SAR radar image geometric parameters (such as satellite orbit angle and angle of incidence) and DEM data, and removes them accordingly. Although this method, based on imaging principles, has certain theoretical advantages, it requires precise acquisition of radar imaging parameters and mathematical modeling, resulting in a complex processing flow and considerable application difficulty.

[0006] The HAND method uses DEM data to calculate the relative height of terrain. When the HAND threshold is properly set, it can effectively screen out non-water areas. Other studies have attempted to optimize hillshade removal using digital surface model (DSM) data. For example, a method combining topological separation with DSM local search can effectively eliminate most misclassified areas, but jagged noise still exists at the boundaries of some water areas.

[0007] The slope threshold method has been widely used for hill shadow removal due to its simplicity and efficiency. This method calculates slope based on a DEM and sets a slope threshold to distinguish hill shadow areas. However, the slope threshold method relies on the user to manually set the threshold, which is highly subjective and empirical. The fixed threshold setting lacks terrain adaptability, hindering stable model migration and automated processing.

[0008] In summary, existing methods for removing hillshade from SAR images all have varying degrees of limitations in their theoretical models, processing workflows, and practical applicability. The formation mechanism method is theoretically robust but operationally cumbersome; the HAND method is computationally convenient but relies on limited information; and the slope method is efficient but lacks adaptive thresholds. All three methods struggle to achieve a balance between accuracy, adaptability, and ease of use across scales and terrains. Summary of the Invention

[0009] The purpose of the present invention is to provide a dynamic threshold removal method for SAR image hill shadows based on an inverse exponential function, so as to solve the misclassification problem caused by the "different objects with the same spectrum" phenomenon of hill shadows in existing SAR image water body extraction, especially the problems of poor adaptability and high false rejection rate of the fixed slope threshold method in complex terrain areas.

[0010] To achieve the above object, the present invention provides a method for removing hill shadows from SAR images using a dynamic threshold based on an inverse exponential function, comprising the following steps:

[0011] S1. Acquire SAR images, digital elevation data, and optical images of the corresponding time, preprocess the acquired data, unify the spatial resolution, and project them into the same spatial coordinate system;

[0012] S2. Based on SAR imagery, water areas are initially extracted using a dual-polarization water index or fixed threshold segmentation. The elevation and slope of each pixel are calculated using digital elevation data. Sample points are randomly generated within the initially extracted water area, and corresponding elevation and slope attributes are assigned to the sample points. A sample dataset is then manually interpreted using optical imagery to generate the sample dataset. The sample dataset contains two types of samples: hill shadow and water.

[0013] S3. Remove outliers from the sample data set using the interquartile range method, perform thinning on the sample points, calculate the dividing point between the two types of sample points in the spatial rectangular coordinate system, construct an inverse exponential dividing function model, and then use the dividing function model to distinguish between mountain shadows and water bodies.

[0014] 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%, so as to maintain the true distribution of the hill shadow and water samples.

[0015] Preferably, calculating the dividing point of the two types of sample points in S3 includes calculating all distances between the two types of sample points, selecting several groups of sample points with small distances, and taking the midpoint of the distance as the dividing point to determine the dividing function model.

[0016] Preferably, when calculating the dividing point of the two types of sample points in S3, the sample points are first converted from the elevation-slope coordinate system to the plane rectangular coordinate system, and then the Euclidean distance of the two types of sample points is calculated to obtain the corresponding dividing point, which is then converted to the elevation-slope coordinate system, an inverse exponential curve is introduced, and a dividing function model is constructed.

[0017] Preferably, the inverse exponential demarcation function model in S4 is expressed as follows:

[0018] ;

[0019] Where, 、 are the parameters of the boundary function model, Indicates elevation, Indicates slope.

[0020] Preferably, constructing the inverse exponential demarcation function model includes optimizing the parameters of the demarcation function model using a grid search method. and ,as follows:

[0021] First, according to the cutoff point, the parameters are determined by local grid search and The interval of each parameter is linearly divided to generate candidate parameter values;

[0022] Then, a global grid search is used to traverse each set of candidate parameter values, and the classification rules of the boundary function model are applied to distinguish between hill shadows and water bodies;

[0023] Afterwards, the classification performance of the set of candidate parameter values ​​is evaluated by calculating the accuracy between the classification results and the true labels, and the optimized parameters are obtained. and , thereby determining the boundary function model.

[0024] Therefore, the present invention adopts the above-mentioned SAR image hill shadow dynamic threshold removal method based on the inverse exponential function, which has the following technical effects:

[0025] (1) The present invention automatically determines the optimal parameter combination through grid search and constructs an inverse exponential demarcation function model without the need to manually set a fixed threshold, significantly reducing dependence on user experience; at the same time, the inverse exponential demarcation function model supports rapid deployment and large-scale automated processing on platforms such as Google Earth Engine (GEE), achieving automation and parameter adaptation.

[0026] (2) Compared with the formation mechanism method which requires precise modeling and the HAND method which requires manual parameter setting, the present invention has a clear structure and standardized steps, does not require tedious geometric simulation and local calculation, has high operating efficiency, can achieve fast operation and stable result output, and is particularly suitable for flood disaster monitoring tasks in emergency response scenarios.

[0027] (3) The inverse exponential function proposed in this invention has the ability to adjust nonlinear boundaries and can dynamically adjust the slope discrimination conditions according to different elevations, thus avoiding the phenomenon that real water bodies are mistakenly eliminated due to fixed thresholds in mountainous areas. This effectively improves the integrity and reliability of the extraction results and has a strong ability to protect the integrity of water bodies.

[0028] (4) The present invention can be directly integrated into flood monitoring and early warning systems, providing more timely and accurate remote sensing data support for government emergency management, meteorology, water conservancy, ecology and other related departments; when sudden flood disasters occur, it can realize efficient and automatic extraction of flooded areas, providing a decision-making basis for emergency dispatch and personnel evacuation, and has broad application prospects and disaster reduction value.

[0029] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a flow chart of the method for removing hill shadows from SAR images using dynamic thresholds based on the inverse exponential function.

[0031] Figure 2 Schematic diagram of calculating the demarcation midpoint of sample points after thinning in an embodiment of a method for dynamic threshold removal of hill shadows in SAR images based on an inverse exponential function;

[0032] Figure 3 The invention is an inverse exponential boundary function model in an embodiment of a method for removing hill shadows from SAR images by dynamic thresholding based on an inverse exponential function;

[0033] Figure 4This is a schematic diagram of an embodiment of a method for removing hill shadows from SAR images using a dynamic threshold value based on an inverse exponential function, in which an inverse exponential boundary function model is applied in an elevation-slope coordinate system to distinguish between water sample points and hill shadow sample points;

[0034] Figure 5 The invention is a SAR flood extraction map before monitoring the mountain shadow in an embodiment of a method for removing the mountain shadow of a SAR image based on a dynamic threshold value of an inverse exponential function;

[0035] Figure 6 This is a SAR flood extraction image after monitoring mountain shadows in an embodiment of a method for dynamic threshold removal of mountain shadows in SAR images based on an inverse exponential function, wherein black represents mountain shadows and red represents floods;

[0036] Figure 7 These are comparative analysis results of different models in an embodiment of a method for dynamic threshold removal of hill shadows in SAR images based on an inverse exponential function, wherein (a) is an optical image, (b) is the method of the present invention, (c) is the HAND method, and (d) is the formation mechanism method. DETAILED DESCRIPTION

[0037] The present invention can be explained in more detail by the following examples. 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 examples.

[0038] Example 1

[0039] Existing hill shadow removal methods have limitations: (1) The formation mechanism method is computationally complex and highly parameter-dependent, making it difficult to deploy efficiently; (2) The HAND method only considers elevation information and is prone to mistakenly deleting water bodies; (3) Although the slope threshold method is efficient, the fixed threshold does not have adaptive capabilities and is unstable under different terrain conditions, which can easily reduce the extraction accuracy.

[0040] To address the problems existing in the prior art, this paper provides a dynamic threshold removal method for hill shadows in SAR images based on an inverse exponential function. This method aims to improve the accuracy and automation of hill shadow removal in SAR flood monitoring by constructing an elevation-slope feature space and introducing an inverse exponential function to establish classification boundaries. This method introduces dynamic adjustment of the slope threshold and adaptive terrain segmentation, thereby improving the accuracy and automation of hill shadow removal in SAR flood monitoring. The method is suitable for rapid flood extraction tasks in large-scale complex terrains. (See [1] for details.) Figure 1 .

[0041] This example mainly uses three types of data: Sentinel-1 SAR imagery, digital elevation data (SRTM), and Sentinel-2 optical imagery. The core idea is to construct an "elevation-slope" feature space, introduce an inverse exponential function as a dynamic classification boundary function, and combine it with a grid search algorithm to achieve optimal parameter selection and construct a water / mountain shadow boundary function.

[0042] Whether the demarcation function can accurately remove hill shadows depends on the construction of the sample dataset. The goal of this stage is to extract flood water areas and construct geographic sample points with elevation-slope characteristic information to provide a data foundation for model training.

[0043] In the first stage, the water area is extracted.

[0044] In this example, Sentinel-1 SAR imagery was retrieved using the Google Earth Engine (GEE) platform. The polarization modes were VV and VH, and the spatial resolution was 10 meters. The imagery was acquired on August 5, 2023, during a period of flooding. The Sentinel-1 SAR imagery retrieved by GEE has already been preprocessed for thermal noise removal, radiometric calibration, and terrain correction, eliminating the need for manual data preprocessing.

[0045] Based on Sentinel-1 SAR imagery, the Sentinel-1 Dual-Polarized Water Index (SDWI) is used to extract water bodies. This index calculates the difference between Sentinel-1 dual-polarization (VV and VH) data, enhancing water body characteristics. The SDWI index is calculated as follows:

[0046] ;

[0047] Where VH and VV are Sentinel-1 dual-polarization backscatter data; SDWI is the result of band mathematical operation. Pixels with a calculated result greater than 0 are considered water bodies, resulting in a water / non-water binary map.

[0048] In other embodiments, the water body area may be preliminarily extracted using a fixed threshold method in the prior art.

[0049] The second stage is to construct a sample data set.

[0050] In this example, the Digital Elevation Model (DEM) data from the SRTM dataset is used through the GEE platform, with a spatial resolution of 30 meters. To ensure spatial compatibility between data of varying spatial resolutions, the 30-meter DEM data is resampled to 10 meters, and all data is uniformly converted to the GCS_WGS_1984 projection.

[0051] Based on the SRTM dataset, the elevation and slope information for each pixel in the study area was calculated. Based on the study area and a reasonable sample density, this example generated 7,000 random sample points within the SDWI water mask and assigned elevation and slope attributes to all of them. ArcMap software was then used to assist in interpretation, using contemporaneous Sentinel-2 optical imagery (taken on August 15th). Each sample point was manually visually annotated with its true category (hill shadow or water). This ultimately resulted in a sample set with two-dimensional feature (elevation and slope) classification labels, including approximately 1,737 water points and 5,263 hill shadow points.

[0052] Due to issues with SRTM data measurement accuracy and spatial resolution, slope calculations can be affected, leading to outliers. However, most outliers are due to human visual misinterpretation. Data measurement errors and visual interpretation errors are often random, which can cause the data distribution to deviate from normality. To address this issue, this example uses the interquartile range (IQR) method to remove outliers from the scatter plot. This method is simple to operate, easy to implement, highly robust, and less susceptible to extreme values ​​in the dataset. Because water samples are primarily concentrated in areas with lower elevations and slopes, while shadow samples are more widely distributed, exhibiting a skewed distribution, traditional IQR methods can misclassify a large number of normal data points as outliers. Therefore, in this example, the quartiles Q1 and Q3 are set to 10% (0.1) and 90% (0.9), respectively. This eliminates some outliers while maintaining sample integrity, retaining enough sample points to represent their true distribution. A total of 42 sample points were removed: 11 water sample points and 31 hillshade sample points.

[0053] In order 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 the outliers are eliminated, the number of sample points is still huge, and it is difficult to directly calculate the dividing 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. This is 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, under 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:

[0054] (1) Calculate the coordinate range of the water point data, then take the coordinate range of the shadow point data into account, and finally obtain a global coordinate range that can contain all data points. The purpose of this is to ensure that all data points can be correctly mapped to the new coordinate system in the subsequent coordinate transformation to avoid data loss.

[0055] (2) A linear mapping function is defined that maps any value in the original coordinate range to the new target range. This mapping is order-preserving, meaning that the relative positional relationships between the original data points are preserved in the new coordinate system. The mathematical principle is to achieve range conversion through scaling and translation.

[0056] (3) Using the matplotlib library, a scatter plot was created to visualize the transformed water points and shadow points in the new Cartesian coordinate system. Figure 2 The blue dots represent water bodies, the orange dots represent mountain shadows, and the horizontal and vertical coordinates range from 0 to 5, forming a standard first quadrant plane rectangular coordinate system.

[0057] Then, the sample points are assigned new coordinate values ​​in the new coordinate system, 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 while reducing the amount of calculation. Figure 2 In this embodiment, the six groups of sample points with the smallest distance are selected, and the midpoint of the distance between the two types of sample points is calculated as the dividing point between the two types of samples. This is used to construct a boundary function model, provide initial conditions for function fitting, and ensure that the boundary function accurately delineates the mountain shadow and water area. This method is of key significance in model construction. On the one hand, through coordinate system conversion 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 fit of the function curve to the real classification boundary.

[0058] Existing technologies generally use linear functions as thresholds to distinguish between hill shadows and water bodies. However, this method lacks terrain adaptability, making it difficult to migrate models stably and automate processing. To address this issue, this example uses an inverse exponential function as the demarcation function model. The morphological characteristics of this function can more accurately fit the boundaries between water and hill shadow sample points, thereby improving classification accuracy. Figure 3 .

[0059] In the elevation and slope coordinate system (see Figure 4 ), inverse exponential function Parameters in and Has clear physical meaning, its parameters The size of determines the final horizontal position of the function curve, that is, when the elevation As it approaches infinity, the slope The value will gradually approach This characteristic can effectively simulate the disappearance of mountain shadows in lower slope areas. As a fixed threshold to remove hill shadows, pixels exceeding this threshold are identified as shadow noise and removed. Especially in areas with high elevation but low slope, such as river areas in mountainous areas, the parameter This prevents these areas from being misidentified as hill shadows.

[0060] parameter This controls the decay rate of the function. The value will make the function The value decays quickly when it is small, due to the slope The value range does not exceed 90°, the elevation The value will not fall below a certain value. In other words, there is a hillshade elevation threshold in the inverse exponential function model. Hillshades below this elevation threshold will not be misidentified as water bodies. This is consistent with the fact that hillshades do not exist in low-altitude areas such as plains.

[0061] Compared with the linear function, the concave curve shape presented by the inverse exponential function provides stronger fitting ability, especially when processing complex terrain data. This nonlinear curve can more accurately describe the boundary between water bodies and mountain shadows.

[0062] Then, the coordinate system is converted back to the elevation-slope coordinate system, and the thinned-out sample points are restored to prepare for the optimization parameters. and , better use the inverse exponential function to distinguish the two types of sample points.

[0063] In optimizing parameters and In this embodiment, the grid search method is used to discretize the parameters of the model and perform exhaustive search one by one on the pre-set parameter grid to find the optimal parameter combination. It is specifically divided into two parts:

[0064] The first part is to set the parameter search range, parameters The interval is set to [4,6], the parameter The interval is set to [150, 180]. The selection of the interval is not random, but is based on the calculated cutoff value, the shape of the inverse exponential function curve, and the determination of the parameters and The upper and lower limits of the values ​​are taken, and then the obtained interval values ​​are rounded off to determine the above search interval, as follows:

[0065] First, based on the calculated 6 groups of demarcation midpoints, each group of midpoints is used as the representative demarcation point, and the inverse exponential demarcation function model is used to construct a local grid search model. In the local grid search, the parameters are systematically adjusted within the set parameter candidate set. and , with the optimization goal of maximizing classification accuracy, determine the local optimal parameter combination that can make the inverse exponential boundary function model optimally divide water bodies and mountain shadows. Taking the first midpoint as an example, fix the coordinates of the midpoint and use grid search to find the parameters that can accurately classify the point and have the highest classification accuracy in its local neighborhood. and Following this method, the same local grid search was performed on the remaining five groups of midpoints, and finally six groups of local optimal parameter results were obtained.

[0066] Then, the six groups of local optimal parameters are statistically analyzed to extract the minimum and maximum values ​​of parameters a and b. In order to retain enough search space to avoid underfitting, the boundary values ​​are rounded by truncation in this embodiment to determine the search interval of the model parameters 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.

[0067] In the second part, after determining the parameter search interval, we continue to use the grid search method within the above interval based on the entire sample data. By maximizing the objective function of overall classification accuracy, we finally obtain the overall optimal parameter combination of the model, as follows:

[0068] First, a linear partition is performed between the intervals [4,6] and [150,180] to generate a series of candidate parameter values. After traversing each candidate parameter pair, the classification rule is applied, that is, when the slope value of the sample is greater than the function value , it is classified as hill shadow (label is 1), otherwise it is classified as water body (label is 0).

[0069] Then, for each parameter combination, the accuracy between the classification result and the true label is calculated to evaluate the classification performance of the combination. Finally, the parameter combination that can maximize the accuracy is selected as the optimal parameter of the model, and the parameter and The optimal value of .

[0070] Through the grid search strategy of the above two parts, the parameter space is effectively narrowed by local midpoint samples, which improves the computational efficiency of model optimization. At the same time, through global optimization of all samples, the classification accuracy of the model and its applicability under complex terrain conditions are guaranteed.

[0071] After multiple parameter optimizations and model adjustments, the model ultimately achieved an optimal accuracy of 0.98 on the test dataset, correctly identifying 1,737 water pixels and 5,263 hill shadow pixels, with only a small number of misclassified pixels. The misclassified samples included 35 hill shadow pixels that were misclassified as water and 105 water pixels that were misclassified as hill shadow. The Kappa coefficient was 0.95, and the overall accuracy reached 98%. The optimal parameters determined by the network search method in this embodiment are 、 , then the optimal model is:

[0072] .

[0073] The high accuracy of the model is largely due to the good match between the mathematical model of the inverse exponential function and the distribution of data characteristics. After removing the sample outliers, the characteristic differences between samples are more significant, making the classification boundaries clearer, and the inverse exponential function model can also divide the samples more accurately. In addition, and The two parameters reached the optimal value. The optimization of the parameters enables the inverse exponential function model to better adapt to the data characteristics during the training process, thereby improving the classification effect.

[0074] In the model application, SDWI (Water Dual Polarization Index) is first used to enhance water features, and then a suitable threshold is set to perform binarization processing to extract the flooded area. 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 northwestern mountainous area of ​​the study area. These areas appear in the figure as patchy water distributions that are inconsistent with the actual water body morphology. In order to distinguish between real water bodies and mountain shadows, this embodiment calls the SRTM digital elevation model (DEM) data, assigns the corresponding elevation and slope information to each pixel in the flood extraction results, and associates the elevation and slope values ​​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 water body area of ​​the image is substituted into the function. If the slope value (Slope) of the pixel point is greater than the function value , it is determined to be a mountain shadow and is divided into a non-water area. By this method, in the process of extracting water bodies from SAR images, the interference of mountain shadows on the results is eliminated. Figure 6 In other embodiments, the model obtained by the present invention can be directly transferred to remote sensing image processing software such as ENVI and Arcmap for application.

[0075] Example 2

[0076] In order to verify the effect of the inverse exponential boundary function model in the present invention in removing hill shadows, this embodiment selects two widely used and highly representative methods for comparative analysis: the formation mechanism method and the nearest neighbor river relative height HAND method.

[0077] See Figure 7 Taking reservoirs in mountainous areas as an example, the formation mechanism method is less effective, leaving behind a significant amount of mountain shadows and incorrectly deleting water bodies. Furthermore, this method is computationally intensive and complex, making it unsuitable for rapid response, especially in applications requiring real-time data processing, such as floods. Despite its simplicity, HAND can also mistakenly delete water bodies (such as the northeast corner of a reservoir). This is because it only considers elevation features, making it easy to misidentify water bodies as non-water bodies at the edges of mountainous water bodies, affecting their integrity. Furthermore, the HAND method requires pre-setting a threshold, which relies on empirical judgment, leading to inaccurate threshold selection and further compromising the integrity and accuracy of water bodies.

[0078] In contrast, this embodiment adopts an inverted exponential boundary function model, which can comprehensively consider the dual characteristics of elevation and slope, and improves the fixed slope threshold method so that it can adaptively adjust the threshold according to the terrain characteristics, thereby improving the adaptability and accuracy of the model in complex terrain and avoiding errors and omissions caused by fixed threshold settings; at the same time, the application process of the inverted exponential boundary function model is simple and efficient, which greatly reduces user participation and complexity, and reduces dependence on experience judgment.

[0079] Therefore, the present invention adopts the above-mentioned SAR image mountain shadow dynamic threshold removal method based on the inverse exponential function, which can effectively eliminate the false water area originally misjudged due to terrain shadow, and improve the authenticity and consistency of the spatial distribution of water bodies, especially in complex terrains such as mountainous areas and piedmont plains.

[0080] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A dynamic threshold removal method for hill shadows in SAR images based on an inverse exponential function, characterized in that: The following steps are involved: S1. Acquire SAR images, digital elevation data, and optical images of the corresponding time, preprocess the acquired data, unify the spatial resolution, and project them into the same spatial coordinate system; S2. Based on SAR imagery, water areas are initially extracted using a dual-polarization water index or fixed threshold segmentation. The elevation and slope of each pixel are calculated using digital elevation data. Sample points are randomly generated within the initially extracted water area, and corresponding elevation and slope attributes are assigned to the sample points. A sample dataset is then manually interpreted using optical imagery to generate the sample dataset. The sample dataset contains two types of samples: hill shadow and water. S3. Remove outliers from the sample dataset using the interquartile range method and perform thinning on the sample points. Calculate the dividing point between the two types of sample points in a spatial rectangular coordinate system, construct an inverted exponential dividing function model, and then use this dividing function model to distinguish between hill shadows and water bodies. Among them, the inverted exponential boundary function model is expressed as follows: ； Where, 、 are the parameters of the boundary function model, Indicates elevation, Represents the slope; when the slope value of the sample point is greater than the function value y, it is classified as hill shadow, otherwise it is classified as water body.

2. The SAR image hill shadow dynamic threshold removal method based on the inverse exponential function according to claim 1 is characterized in that: The first quartile Q1 of the interquartile range method in S3 is set to 10%, and the third quartile Q3 is set to 90% to maintain the true distribution of the hill shadow and water samples.

3. The SAR image hill shadow dynamic threshold removal method based on the inverse exponential function according to claim 1 is characterized in that: In S3, the dividing point between the two types of sample points is calculated, including calculating all distances between the two types of sample points, selecting several groups of sample points with small distances, and taking the midpoint of the distance as the dividing point to determine the parameters of the dividing function model.

4. The method for removing hill shadows from SAR images based on a dynamic threshold value of an inverse exponential function according to claim 3, wherein: When calculating the dividing point between two types of sample points in S3, the sample points are first converted from the elevation-slope coordinate system to the plane rectangular coordinate system, and then the Euclidean distance between the two types of sample points is calculated to obtain the corresponding dividing point, which is then converted back to the elevation-slope coordinate system, and the inverse exponential curve is introduced to construct the dividing function model.

5. The SAR image hill shadow dynamic threshold removal method based on inverse exponential function according to claim 1 is characterized in that: Constructing the inverted exponential boundary function model includes using the grid search method to optimize the parameters of the boundary function model and ,as follows: First, according to the cutoff point, the parameters are determined by local grid search and The interval of each parameter is linearly divided to generate candidate parameter values; Then, a global grid search is used to traverse each set of candidate parameter values, and the classification rules of the boundary function model are applied to distinguish between hill shadows and water bodies; Afterwards, the classification performance of the set of candidate parameter values ​​is evaluated by calculating the accuracy between the classification results and the true labels, and the optimized parameters are obtained. and , thereby determining the boundary function model.

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