Landslide extraction method based on multi-source remote sensing data fusion

Abstract

The present application relates to the technical field of geological disaster monitoring and remote sensing image processing, and specifically discloses a landslide extraction method based on multi-source remote sensing data fusion. The method unifies the resolution and projection of optical remote sensing images, synthetic aperture radar data and digital elevation model data, constructs a multi-dimensional feature system containing vegetation attenuation factors, terrain factors and SAR dynamic factors; adopts entropy weight method combined with physical correction and variation coefficient method to dynamically allocate factor weights, constructs a landslide risk index, designs an adaptive threshold model based on data distribution characteristics, dynamically optimizes the segmentation threshold through data distribution characteristics, spatial context features and threshold reliability, and finally realizes accurate extraction of landslide areas. The present application solves the problems of low precision and poor adaptability caused by single data source, fixed threshold and unreasonable weight allocation in traditional landslide extraction methods, improves the accuracy and robustness of landslide extraction under complex terrain conditions, and provides reliable technical support for post-earthquake disaster assessment and emergency response.

Description

Technical Field

[0001] This invention relates to the field of remote sensing image processing technology, specifically a landslide extraction method based on multi-source remote sensing data fusion. Background Technology

[0002] With the rapid development of remote sensing technology and geographic information science, landslide disaster monitoring has gradually evolved from traditional ground surveys to integrated space-air-ground observation. The ability to acquire multi-source data, such as optical satellites, synthetic aperture radar (SAR), and digital elevation models (DEM), has been continuously improved, providing rich surface information for landslide monitoring. Optical data can capture changes in vegetation cover, SAR data can penetrate clouds and fog to obtain dynamic surface structures, and DEMs support the extraction of topographic factors such as slope and curvature. Simultaneously, the maturity of spatial data processing technologies has made spatiotemporal alignment, feature fusion, and quantitative analysis of multi-source data possible, laying a technological foundation for the early identification and dynamic assessment of landslide hazards.

[0003] Traditional landslide identification methods still suffer from significant bottlenecks. Existing methods often rely on single types of data, such as monitoring vegetation changes using only optical imagery, analyzing topographic features solely based on DEMs, or detecting surface deformation using only SAR data. These methods neglect the fact that landslides are actually a complex process driven by the coupling of multiple factors, including topography, vegetation, and surface physical properties, leading to incomplete identification and insufficient interpretability of potential landslides. When extracting landslide areas, traditional methods generally employ fixed thresholds, empirical thresholds, or single automatic thresholds, lacking targeted analysis of the distribution of landslide index data for specific areas. This "one-size-fits-all" segmentation strategy struggles to address the differences in index value distribution caused by different geographical environments and landslide scales, resulting in numerous spatial misclassifications or omissions in the extraction results.

[0004] To address the aforementioned issues, this paper proposes a landslide extraction method based on multi-source remote sensing data fusion. This method comprehensively utilizes optical remote sensing data, SAR data, and DEM data to construct a multi-dimensional feature set including vegetation attenuation factors, topographic factors, and SAR dynamic factors. Furthermore, it employs entropy weighting and coefficient of variation to quantify the weights of each factor, constructing a landslide risk index (LRI). By combining spatial context analysis and an adaptive threshold based on data distribution characteristics, the LRI is binarized, achieving accurate extraction of landslide areas through multi-factor synergy. This effectively solves the problems of single data source and poor threshold adaptability in traditional methods. Summary of the Invention

[0005] 1. A landslide extraction method based on multi-source remote sensing data fusion, characterized by comprising the following steps:

[0006] S1: Acquire optical remote sensing images, synthetic aperture radar data, and digital elevation model data of the target area before and after the landslide, and standardize all data to ensure spatial alignment by unifying resolution and projection.

[0007] S2: Based on the preprocessed optical remote sensing image, calculate the normalized vegetation index change ΔNDVI, where ΔNDVI is the difference between the normalized vegetation index of the first time phase and the normalized vegetation index of the second time phase. Positive values ​​are retained and normalized to obtain the vegetation attenuation factor. Based on the preprocessed digital elevation model data, extract terrain factors, including slope, curvature, and terrain roughness. Each terrain factor is normalized. Based on the preprocessed synthetic aperture radar data, calculate the SAR dynamic factor, which includes the SAR variation index and SAR spatial consistency. The SAR variation index is obtained by weighting the polarization logarithm ratio, polarization ratio change, and texture change. SAR spatial consistency is calculated using the standard deviation of the SAR variation index within a 5×5 window. Each SAR dynamic factor is normalized.

[0008] S3: The initial weights of slope, curvature and roughness are calculated using the entropy weight method. The slope weight ratio is increased through physical correction to obtain the final terrain factor weights. The weights of the SAR dynamic factors are calculated based on the coefficient of variation. The weight of SAR spatial consistency is the ratio of the sum of its coefficient of variation and the coefficient of variation of the SAR change index. The weight of the SAR change index is the difference between 1 and the ratio.

[0009] S4: Calculate static terrain risk based on the terrain factors and their weights, calculate SAR dynamic risk based on the SAR dynamic factors and their weights, and construct landslide risk index LRI by combining vegetation attenuation factor.

[0010] S5: An adaptive threshold based on data distribution characteristics is calculated by weighted fusion of the OTSU threshold, percentile threshold, dynamic scaling threshold, and spatial adjustment factor, while incorporating range constraints to ensure reasonableness. The skewness, kurtosis, data density features, and spatial context weights of the LRI index for all pixels in the target region are calculated. The basic threshold is then obtained using the OTSU algorithm. The basic threshold was obtained using the percentile method. The basic threshold is obtained using the LRI maximum value dynamic scaling method. The extraction ratio and data density near each basic threshold are calculated to obtain a threshold reliability score. Based on the data distribution characteristics and the threshold reliability score, the weights of the three basic thresholds and the spatial context adjustment factor are dynamically allocated. By weighted fusion of the basic thresholds and the spatial context adjustment factor, combined with range constraints, an adaptive threshold based on the data distribution characteristics is obtained. ;

[0011] S6: Based on the threshold in S5, the LRI index is binarized. Small area noise and isolated points in the binarization result are removed by morphological opening operation. Small holes and connection fracture areas in the result after opening operation are filled by morphological closing operation to obtain the final landslide extraction result.

[0012] Furthermore, in S4, the calculation method for the LRI index is as follows:

[0013]

[0014] in, Indicates static terrain risk factor, This represents the vegetation decay factor, which is the normalized change in the vegetation index. Indicates the dynamic risk factor of SAR;

[0015] Calculate static terrain risk factors Its formula is:

[0016]

[0017] in, , , These represent the final terrain factor weights for slope, curvature, and roughness obtained in step S3, respectively. This represents the normalized slope. This represents the normalized curvature. This represents the normalized terrain roughness.

[0018] Calculate SAR dynamic risk factors Its formula is:

[0019]

[0020] in, This represents the SAR spatial consistency weight obtained in step S3. This represents the SAR change index weights obtained in step S3. This indicates the spatial consistency of the normalized SAR. This represents the normalized SAR change index.

[0021] Furthermore, in S5, the adaptive threshold calculation method based on data distribution characteristics uses a weighted fusion of the OTSU threshold, percentile threshold, dynamic proportion threshold, and spatial adjustment factor, while incorporating range constraints to ensure rationality. The formula is as follows:

[0022]

[0023] in, This represents an adaptive threshold based on data distribution characteristics. This represents the base threshold obtained by the OTSU algorithm. This represents the preset percentile baseline threshold for valid LRI data. This represents the dynamic scaling threshold of the maximum LRI value. Indicates the spatial adjustment factor. This represents the normalized OTSU threshold weight. This represents the percentile threshold weight after normalization. This represents the dynamic proportional threshold weight after normalization. This represents the threshold weight of the spatial context adjustment factor after normalization.

[0024] First, innovative indicators are constructed to quantify the distribution characteristics and spatial heterogeneity of effective LRI data, providing a basis for threshold optimization. Among them, the data density indicator breaks through the traditional evaluation method that relies on the entire range of data. By using the ratio of interquartile range to data range, it reduces the interference of extreme values ​​and more accurately reflects the data aggregation. Its formula is:

[0025]

[0026] in, This represents data density; a larger value indicates that the effective data distribution of LRI is more concentrated. This represents the 75th percentile of the significant data in the LRI. This represents the 25th percentile of the significant data in the LRI. This represents the maximum value of valid LRI data. This represents the minimum value of valid LRI data. Indicates a pre-defined small positive number;

[0027] The spatial context weight is calculated, which breaks through the limitation of traditional thresholds that rely solely on numerical distribution. It combines the dispersion of effective LRI data with the overall level of spatial heterogeneity quantification to reflect the impact of landslide spatial distribution differences on the threshold. The formula is as follows:

[0028]

[0029] in, Represents spatial context weights, This represents the set of valid LRI data after removing invalid values. This represents the function for calculating standard deviation. This represents the function for calculating the mean. This is a preset maximum value used to limit the weight range. Preset to small positive numbers;

[0030] The dynamic scaling threshold for the maximum LRI value is calculated. This threshold breaks away from the traditional fixed scaling design and dynamically adjusts the scaling factor based on the kurtosis of the effective LRI data to adapt to different data distribution characteristics. The formula is as follows:

[0031]

[0032] in, This represents the dynamic scaling threshold of the maximum LRI value. This represents the maximum value of valid LRI data. Indicates the dynamic proportional base coefficient. This represents the kurtosis adjustment factor; The kurtosis value represents the effective data of LRI, used to quantify the steepness of the data distribution. This represents the kurtosis constraint coefficient, which prevents excessively large kurtosis from causing abnormal scaling factors.

[0033] Next, the reliability score for each individual threshold is calculated. This score combines the "reasonableness of the extraction ratio" and the "uniformity of data distribution near the threshold," avoiding the limitations of a single indicator evaluation and providing a basis for dynamic weight allocation. The formula is as follows:

[0034]

[0035] in, This represents the reliability score of a single threshold; a higher value indicates a stronger applicability of the threshold. This represents the weighting coefficient of the extracted percentage score. This represents the weighting coefficient of the data density score near the threshold, and , The score represents the extraction ratio, used to assess the rationality of the extracted landslide area. This represents the data density score near the threshold, assessing the uniformity of data distribution;

[0036] Next, the OTSU threshold weight is calculated. This weight breaks away from the traditional equal weight design and dynamically adjusts the proportion based on the reliability score of the OTSU threshold and the skewness of the valid LRI data. Greater skewness indicates greater data asymmetry, requiring a reduction in the OTSU threshold weight to overcome its limitations. The formula is as follows:

[0037]

[0038] in, Indicates the OTSU threshold weight. The reliability score represents the OTSU threshold. The total reliability score is the sum of the reliability scores for the OTSU threshold, percentile threshold, and dynamic proportion threshold, along with the spatial context weights. This represents the skewness value of the valid LRI data. As the lower limit of the weight, This represents the upper limit of the OTSU threshold weight. This is the kurtosis constraint coefficient, which controls the magnitude of the influence of skewness on the weights;

[0039] Simultaneously, a percentile threshold weight is calculated. This weight combines the reliability score of the percentile threshold with the proportion of kurtosis in the valid LRI data for dynamic adjustment, adapting to differences in data centrality. The formula is as follows:

[0040]

[0041] in, Indicates percentile threshold weight. The reliability score represents the percentile threshold. This represents the upper limit of the percentile threshold weight. This is the kurtosis constraint coefficient, which adapts to the tolerance of percentile thresholds to kurtosis. , , The meaning is consistent with the OTSU threshold weight formula;

[0042] The formula for calculating the dynamic proportional threshold weight is as follows:

[0043]

[0044] in, Indicates dynamic proportional threshold weight. The reliability score represents the dynamic scaling threshold.

[0045] The formula for calculating the spatial context adjustment factor weight is as follows:

[0046]

[0047] in, Indicates the spatial context adjustment factor weights;

[0048] The above weights are normalized using the following formula:

[0049]

[0050]

[0051]

[0052]

[0053] in, This represents the normalized OTSU threshold weight. This represents the percentile threshold weight after normalization. This represents the dynamic proportional threshold weight after normalization. This represents the threshold weight of the spatial context adjustment factor after normalization.

[0054] Next, calculate the spatial adjustment factor, which is used to correct the dynamic scaling threshold. This factor, combined with the variability and mean square of the effective LRI data, improves the robustness of the threshold to data fluctuations. The formula is as follows:

[0055]

[0056] in, Indicates the spatial adjustment factor. This represents the dynamic scaling threshold of the maximum LRI value. For spatial adjustment of the reference coefficient, This represents the variance calculation function. This represents the square of the mean. This is the spatial adjustment coefficient. It is a preset small positive number.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] 1. Traditional landslide detection methods often rely on a single data source, such as using only optical imagery to monitor vegetation changes or relying solely on DEM analysis of topographic features. These methods fail to comprehensively characterize the complex phenomenon of landslides, which involves multiple coupled factors. The LRI index constructed in this invention achieves complementary advantages by integrating optical, SAR, and DEM data. Optical imagery's ΔNDVI accurately captures vegetation attenuation information; SAR data monitors dynamic changes in surface physical properties through polarization ratio, logarithmic ratio, and texture variations; and DEM provides topographic stability factors such as slope and curvature. Through the synergistic effect of topographic risk and vegetation attenuation, it can reduce false detections in gently sloping bare land and farmland areas. Even if vegetation attenuation occurs in these areas, the lack of sufficient topographic risk prevents them from being mistakenly identified as potential landslide hazards.

[0059] 2. Traditional methods often rely on empirical settings or simple mathematical statistics to determine factor weights, lacking physical support and failing to accurately reflect the true contribution of each factor in the landslide incubation and occurrence process, thus affecting the accuracy and reliability of landslide extraction. This invention uses an entropy weighting method combined with physical corrections to determine the weights of topographic factors. While respecting the statistical characteristics of the data, it highlights the core role of slope in landslide formation, making the weight allocation both objective and consistent with geomechanical principles. For SAR dynamic factors, the weight allocation based on the coefficient of variation can adapt to the data characteristics of different regions. In areas with significant SAR signal changes, it automatically increases the weight of the change index, while in areas with obvious spatial consistency characteristics, it strengthens the consistency weight. This weight allocation mechanism demonstrates good adaptability in practical applications, maintaining stable detection performance under different geological environments and climatic conditions.

[0060] 3. Traditional threshold segmentation methods often employ fixed thresholds or single automatic thresholds, resulting in inconsistent performance across different regions and data quality conditions. This invention constructs an adaptive thresholding system based on data distribution characteristics. It quantifies the statistical properties of the dataset by analyzing the skewness, kurtosis, and other distribution characteristics of the LRI index; considers the spatial heterogeneity of images by incorporating spatial context weights; and evaluates the reliability of each basic threshold. Finally, it determines the optimal threshold through dynamic weighted fusion. This mechanism effectively adapts to the differences in data distribution across different terrains, such as mountainous areas, hills, and plains, significantly reducing false negatives and false negatives caused by improper threshold settings. Especially in mountainous areas with complex terrain, it can accurately identify small to medium-sized landslides, avoiding misclassification of steep rock faces as landslides, while ensuring effective detection of potential landslides in gentle slope areas. Attached Figure Description

[0061] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0062] Figure 1 This is a flowchart of an embodiment of the present invention;

[0063] Figure 2 These are optical images of a landslide before and after an embodiment of the present invention;

[0064] Figure 3 This is a normalized result diagram of the vegetation attenuation factor according to an embodiment of the present invention;

[0065] Figure 4 This is a terrain risk result map of an embodiment of the present invention;

[0066] Figure 5 This is a dynamic risk map of SAR according to an embodiment of the present invention;

[0067] Figure 6 This is a distribution map of the LRI landslide sensitivity index according to an embodiment of the present invention;

[0068] Figure 7 This is a diagram showing the landslide detection results according to an embodiment of the present invention. Detailed Implementation

[0069] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0071] like Figure 1 As shown, this invention discloses a landslide extraction method based on multi-source remote sensing data fusion, specifically including the following steps:

[0072] S1: Multi-source data acquisition and standardization processing. Optical images before and after the landslide are shown below. Figure 2 As shown.

[0073] This is used to achieve spatial consistency and uniformity of data, providing a standardized data source for subsequent landslide extraction.

[0074] First, Sentinel-2 optical remote sensing images, Sentinel-1 SAR images, and digital elevation model data of the target area before and after the landslide were acquired. For the optical images, the red band (B04) and near-infrared band (B08) were selected as the core analysis bands due to their high sensitivity to vegetation changes. By reading the pixel matrix of these bands, the reference shape of the study area was determined. , Number of pixel rows (Number of pixel columns).

[0075] All data are standardized with uniform resolution and projection to ensure spatial alignment. A bilinear interpolation algorithm is used to resample non-10-meter resolution bands to ensure that the spatial resolution of all bands matches the reference shape. During resampling, pixel values ​​are calculated based on a weighted average of surrounding pixels, using the following formula:

[0076]

[0077] in, For resampling The pixel value of the location, This is the original band data. The weights are bilinear interpolation weights to ensure that the resampled data retains the integrity of the original surface features.

[0078] The projection uniformly adopts the WGS84 geographic coordinate system (EPSG:4326), and coordinate transformation ensures that all data layers are under the same geographic reference frame. No data values ​​are uniformly set to -9999 to facilitate the selection of valid values ​​in subsequent processing. Spatial consistency checks ensure that the pixel dimensions of all data layers are equal to the reference shape, ultimately forming a standardized multi-source dataset.

[0079] S2: Multidimensional factor calculation and normalization. The normalization results of vegetation attenuation factors are shown in the figure below. Figure 3 As shown.

[0080] Based on the preprocessed multi-source data, feature factors in three dimensions—optical, topographic, and SAR—are calculated separately. Strict normalization is used to ensure the comparability of each factor, laying the foundation for subsequent weight calculations and risk index construction.

[0081] Calculate the normalized vegetation index change based on preprocessed optical images. This factor can effectively reflect the vegetation damage caused by landslides.

[0082] First, the Normalized Difference Vegetation Index (NDVI) for both time phases is calculated using the following formula:

[0083]

[0084] in, This represents the reflectance value in the near-infrared band (B08). This represents the reflectance value for the red band (B04). To avoid numerical anomalies caused by a denominator of 0, special processing rules are set when... hour, The value is 0. The range of NDVI is [-1, 1], with positive values ​​representing vegetation cover and negative values ​​usually corresponding to water bodies or clouds.

[0085] The The difference between the normalized vegetation index (NDI) of the first time phase and the normalized vegetation index of the second time phase is expressed by the following formula:

[0086]

[0087] in, and represent the NDVI values ​​before and after the landslide, respectively. Since landslides primarily cause vegetation destruction, therefore... Negative values ​​are set to 0, and only positive values ​​are retained to obtain the vegetation attenuation factor.

[0088] The vegetation attenuation factor is subjected to minimum-maximum normalization to transform it to the [0,1] range. The formula is as follows:

[0089]

[0090] in, Represents the vegetation attenuation factor, after normalization. The higher the value, the more severe the vegetation damage at that location, and the higher the likelihood of a landslide.

[0091] Three key topographic factors were extracted from the preprocessed DEM data: slope, curvature, and topographic roughness. These factors together reflect the influence of landform on landslide occurrence.

[0092] The slope factor, calculated using GDAL's DEMProcessing tool, reflects the steepness of surface units. The slope calculation is based on the elevation change rate of the DEM data, and the formula is:

[0093]

[0094] in, Indicates the slope factor. and They are respectively and The rate of change of elevation in a direction. Slope values ​​are in degrees; the larger the value, the steeper the terrain.

[0095] The curvature factor is obtained by calculating the second derivative of elevation data and characterizes the surface undulations. The curvature is calculated using the Laplace operator, and its formula is:

[0096]

[0097] in, Represents the curvature factor. and They are respectively and The second derivative of the direction. A positive value represents a convex surface, a negative value represents a concave surface, and a zero value represents a flat surface.

[0098] Terrain roughness through The standard deviation of elevation values ​​within a window, reflecting the microscopic undulations of the Earth's surface, is calculated using the following formula:

[0099]

[0100] in, Indicates terrain roughness, For the first in the window Elevation value per pixel The average elevation within the window. The total number of pixels within the window ( ).

[0101] Each topographic factor is normalized to the range [0,1] using the min-max normalization method, and the formula is as follows:

[0102]

[0103]

[0104]

[0105] in, This represents the normalized slope factor. This represents the normalized curvature factor. Represents the normalized terrain roughness Indicates the slope factor. Represents the curvature factor. It represents the roughness of the terrain, and the curvature is normalized to the absolute value to highlight the degree of surface variation without distinguishing between concave and convex shapes.

[0106] Two key dynamic factors were calculated based on the preprocessed SAR data: the SAR variation index and the SAR spatial consistency. These factors reflect the changes in surface scattering characteristics caused by landslides.

[0107] The SAR variation index is obtained by weighted fusion of three components: VV polarization log ratio, polarization ratio variation, and texture variation. The VV polarization log ratio is obtained by calculating the ratio of VV polarization data from two time phases and taking the logarithm; the formula is as follows:

[0108]

[0109] in, This represents the SAR change corresponding to VV polarization. This represents the VV polarization value after a landslide occurs. This represents the VV polarization value before the landslide. To prevent division by zero for extremely small constants, the absolute value is taken. To highlight the magnitude of the change.

[0110] The polarization ratio change is obtained by calculating the absolute difference between the VV / VH polarization ratios of the two phases, and the formula is as follows:

[0111]

[0112] in, Indicates the change in polarization ratio. This represents the VV polarization value after a landslide occurs. This represents the VV polarization value before the landslide. This represents the VH polarization value after a landslide. This represents the VH polarization value before the landslide. This indicates removing the absolute value.

[0113] Texture variations are calculated by two-phase VV polarization. The absolute difference of the window standard deviation is obtained using the following formula:

[0114]

[0115] in, Indicates texture changes, Indicates VV polarization after landslide Window standard deviation Indicating VV polarization before the landslide Window standard deviation.

[0116] The SAR change index is obtained by weighting the three components with empirical weights of 0.4, 0.4, and 0.2, and the formula is as follows:

[0117]

[0118] SAR spatial consistency passed The standard deviation of the SAR variation index within the window, reflecting the local consistency characteristics of SAR variation, is calculated using the following formula:

[0119]

[0120] in, Indicates SAR spatial consistency. For the first in the window SAR change index value of each pixel The mean of the SAR change index within the window. This represents the total number of pixels within the window.

[0121] Each SAR dynamic factor is normalized to the range [0,1] using the min-max normalization method, and the formula is as follows:

[0122]

[0123]

[0124] in, This represents the SAR change index after normalization. This represents the SAR spatial consistency index after normalization.

[0125] Through the calculation and normalization of the above multi-dimensional factors, standardized features of optical, topographic and SAR dimensions were obtained, providing reliable input data for the subsequent construction of landslide risk index.

[0126] S3: Calculation of terrain factors and SAR dynamic factor weights.

[0127] The initial weights of slope, curvature, and roughness are calculated using the entropy weight method. This method, based on the information entropy theory, can objectively reflect the importance of each factor in landslide risk assessment.

[0128] First, a topographic factor evaluation matrix is ​​constructed. Let the study area have a total of... There are 10 effective pixels, each containing 3 terrain factors, and the formula is as follows:

[0129]

[0130] in, Represents the terrain factor evaluation matrix. Indicates the first The pixel in the first Normalized values ​​for each terrain factor These correspond to slope, curvature, and roughness, respectively.

[0131] Each factor is normalized. Since the topographic factors are all positive indicators (the larger the value, the higher the landslide risk), the formula is as follows:

[0132]

[0133] in, Indicates the first Among the factors, the first one is the... The normalized value of each pixel ensures .

[0134] The entropy value of each factor is calculated using the following formula:

[0135]

[0136] in, Indicates the first The entropy value of each factor, For normalization coefficients, ensure .when At that time, it was stipulated .

[0137] The formula for calculating the difference coefficient for each factor is as follows:

[0138]

[0139] in, The coefficient of variation represents the difference coefficient, reflecting the... The degree of difference among the factors in landslide risk assessment The larger the value, the more information the factor provides, and the greater its weight should be.

[0140] The initial weights of each factor are calculated using the following formula:

[0141]

[0142] in, Indicates the first The initial weights of the factors satisfy the following conditions: .

[0143] The slope weight is increased through physical correction. Considering that slope is the most important topographic factor affecting landslide stability, the slope weight is multiplied by an enhancement factor of 1.2, as shown in the formula:

[0144]

[0145] in, The initial weights representing the slope. This indicates the corrected slope weight.

[0146] The corrected weights are normalized to obtain the final terrain factor weights, and the formula is as follows:

[0147]

[0148]

[0149]

[0150] in, , , Let these represent the final weights for slope, curvature, and roughness, respectively, satisfying... .

[0151] The weights of SAR dynamic factors are calculated based on the coefficient of variation method. This method can reflect the dispersion of each factor's data. The greater the dispersion, the stronger the factor's distinguishing ability, and the higher its weight should be.

[0152] First, calculate the coefficient of variation of the SAR change index, using the following formula:

[0153]

[0154] in, The standard deviation of the SAR change index is represented by... This represents the mean of the SAR change index. The coefficient of variation represents the SAR variation index.

[0155] The coefficient of variation for SAR spatial consistency is calculated using the following formula:

[0156]

[0157] in, The standard deviation representing the spatial consistency of SAR The mean value representing the spatial consistency of SAR. The coefficient of variation represents the spatial consistency of SAR.

[0158] The weight of SAR spatial consistency is calculated based on the coefficient of variation, and the formula is as follows:

[0159]

[0160] in, The weight representing SAR spatial consistency reflects the relative importance of this factor in SAR dynamic risk assessment.

[0161] The weights of the SAR change index are calculated using the following formula:

[0162]

[0163] in, The weights of the SAR change index are represented by the following: .

[0164] The objective weights of topographic factors and SAR dynamic factors were obtained through the above weight calculation method, providing a scientific basis for the subsequent construction of the landslide risk index and ensuring the reasonable contribution of each factor in the comprehensive assessment.

[0165] S4: Construct the Landslide Risk Index (LRI). The topographic risk results are shown in the image below. Figure 4 As shown, the SAR dynamic risk map is as follows: Figure 5 As shown.

[0166] Based on the topographic factor weights and SAR dynamic factor weights calculated in the preceding steps, and combined with the normalized data of each factor, a comprehensive landslide risk index (LRI) is constructed. This index integrates information from three dimensions: topographic stability, vegetation change, and surface dynamic response, and can comprehensively reflect the potential risk of landslides.

[0167] The static topographic risk value characterizes the susceptibility to landslides due to topographic conditions, and is a weighted average of three topographic factors: slope, curvature, and roughness. Its formula is:

[0168]

[0169] in, Indicates static terrain risk. , , These are the normalized slope, curvature, and roughness values, respectively. , , These are the corresponding weights, and they satisfy... .

[0170] The SAR dynamic risk value characterizes the dynamic features of landslides reflected by changes in surface scattering properties and consistency. It is a weighted summary of SAR spatial consistency and SAR variation index. The formula is:

[0171]

[0172] in, Indicates SAR dynamic risk, To ensure the spatial consistency of SAR after normalization. This is the normalized SAR change index. , These are the corresponding weights, and they satisfy... .

[0173] Introducing vegetation attenuation factor This factor reflects the degree of vegetation damage before and after a landslide. Multiplying the static topographic risk by the vegetation attenuation factor yields the topographic-vegetation synergistic component:

[0174]

[0175] in, Indicates the combined topography-vegetation index. Indicates static terrain risk. This represents the vegetation decay factor, reflecting the synergistic effect of topographic factors and vegetation change.

[0176] This component reflects the coupling effect between topographic conditions and vegetation changes: in steep terrain areas, if vegetation is severely damaged, the risk of landslides increases significantly; while in flat areas, even if vegetation is severely damaged, the risk of landslides is relatively low.

[0177] The comprehensive landslide risk index (LRI) is constructed by multiplying the topography-vegetation co-component with the SAR dynamic risk, and its formula is as follows:

[0178]

[0179] in, Indicates the landslide risk index. Indicates static terrain risk. Indicates vegetation attenuation factor. The LRI (Lower Risk Index) indicates the dynamic risk of landslides at that location. A higher LRI value indicates a greater risk of landslides. This index integrates topographic, vegetation, and dynamic SAR information, providing a more comprehensive reflection of the likelihood of landslides.

[0180] Through the above steps, we obtained a landslide risk index that integrates multi-source data, providing a reliable foundation for subsequent adaptive threshold segmentation and landslide extraction. This index not only considers static terrain conditions but also incorporates dynamic change information, enabling more accurate identification of potential landslide areas.

[0181] S5: Calculate the adaptive threshold based on data distribution characteristics

[0182] Based on the spatial distribution characteristics of the landslide risk index (LRI), an adaptive threshold is calculated using a multi-method fusion strategy. Through dynamic weight allocation and spatial context adjustment, the threshold is ensured to adapt to the data distribution characteristics of different regions, thereby achieving accurate segmentation of landslide areas.

[0183] First, innovative indicators are constructed to quantify the distribution characteristics and spatial heterogeneity of effective LRI data, providing a basis for threshold optimization. Among them, the data density indicator breaks through the traditional evaluation method that relies on the entire range of data. By using the ratio of interquartile range to data range, it reduces the interference of extreme values ​​and more accurately reflects the data aggregation. Its formula is:

[0184]

[0185] in, This represents data density; a larger value indicates that the effective data distribution of LRI is more concentrated. This represents the 75th percentile of the significant data in the LRI. This represents the 25th percentile of the significant data in the LRI. This represents the maximum value of valid LRI data. This represents the minimum value of valid LRI data. Indicates a pre-defined small positive number;

[0186] The spatial context weight is calculated, which breaks through the limitation of traditional thresholds that rely solely on numerical distribution. It combines the dispersion of effective LRI data with the overall level of spatial heterogeneity quantification to reflect the impact of landslide spatial distribution differences on the threshold. The formula is as follows:

[0187]

[0188] in, Represents spatial context weights, This represents the set of valid LRI data after removing invalid values. This represents the function for calculating standard deviation. This represents the function for calculating the mean. This is a preset maximum value used to limit the weight range. Preset to small positive numbers;

[0189] Calculate the skewness and kurtosis of the effective LRI data. Skewness reflects the asymmetry of the LRI data distribution, and its formula is:

[0190]

[0191] in, Indicates skewness, quantifying the asymmetry of the data distribution. This represents the mean. This represents the median. The standard deviation is represented by a skewness greater than 0, indicating that the data is right-skewed and has more high-risk values. A skewness less than 0 indicates that the data is left-skewed and has more low-risk values.

[0192] Kurtosis reflects the kurtosis of the LRI data distribution, and its formula is:

[0193]

[0194] in, Kurtosis indicates the steepness of the data distribution. This represents the mean. This represents the median. The standard deviation is represented by kurtosis. A kurtosis greater than 0 indicates that the distribution is more angular and has thicker tails than a normal distribution, while a kurtosis less than 0 indicates that the distribution is flatter and has thinner tails than a normal distribution.

[0195] The OTSU threshold is calculated using the Otsu algorithm. This method is based on the principle of maximizing inter-class variance, and its formula is:

[0196]

[0197] in, For candidate thresholds, and Below and above the threshold respectively pixel ratio, and These are the means of the two classes, respectively.

[0198] Based on the distribution characteristics of LRI data, the 95th percentile is used as the basic threshold, and the formula is as follows:

[0199]

[0200] in, The 95th percentile baseline threshold for valid LRI data. This represents the 95th percentile, meaning that 95% of the valid LRI data points are below this threshold. This threshold effectively captures the high-value regions of the data distribution and is adaptable to different data distribution patterns.

[0201] The dynamic scaling threshold for the maximum LRI value is calculated. This threshold breaks away from the traditional fixed scaling design and dynamically adjusts the scaling factor based on the kurtosis of the effective LRI data to adapt to different data distribution characteristics. The formula is as follows:

[0202]

[0203] in, This represents the dynamic scaling threshold of the maximum LRI value. This represents the maximum value of valid LRI data. Indicates the dynamic proportional base coefficient. This represents the kurtosis adjustment factor; The kurtosis value represents the effective data of LRI, used to quantify the steepness of the data distribution. This represents the kurtosis constraint coefficient, which prevents excessively large kurtosis from causing abnormal scaling factors.

[0204] Next, the reliability score for each individual threshold is calculated. This score combines the "reasonableness of the extraction ratio" and the "uniformity of data distribution near the threshold," avoiding the limitations of a single indicator evaluation and providing a basis for dynamic weight allocation. The formula is as follows:

[0205]

[0206] in, This represents the reliability score of a single threshold; a higher value indicates a stronger applicability of the threshold. This represents the weighting coefficient of the extracted percentage score. This represents the weighting coefficient of the data density score near the threshold, and , The score represents the extraction ratio, used to assess the rationality of the extracted landslide area. This represents the data density score near the threshold, assessing the uniformity of data distribution;

[0207] The formula for calculating the extraction ratio score is as follows:

[0208]

[0209]

[0210] in, The score represents the extraction ratio, used to assess the rationality of the extracted landslide area. This indicates the landslide extraction ratio at the current threshold; the ideal extraction ratio is 0.15. For values ​​above the threshold The number of pixels, This represents the total number of pixels.

[0211] The formula for calculating the data density score near the threshold is as follows:

[0212]

[0213]

[0214] in, This represents the data density score near the threshold, used to assess the uniformity of data distribution. Indicates threshold Nearby area Data point density within;

[0215] Next, the OTSU threshold weight is calculated. This weight breaks away from the traditional equal weight design and dynamically adjusts the proportion based on the reliability score of the OTSU threshold and the skewness of the valid LRI data. Greater skewness indicates greater data asymmetry, requiring a reduction in the OTSU threshold weight to overcome its limitations. The formula is as follows:

[0216]

[0217] in, Indicates the OTSU threshold weight. The reliability score represents the OTSU threshold. The total reliability score is the sum of the reliability scores for the OTSU threshold, percentile threshold, and dynamic proportion threshold, along with the spatial context weights. This represents the skewness value of the valid LRI data. As the lower limit of the weight, This represents the upper limit of the OTSU threshold weight. This is the kurtosis constraint coefficient, which controls the magnitude of the influence of skewness on the weights;

[0218] Simultaneously, a percentile threshold weight is calculated. This weight combines the reliability score of the percentile threshold with the proportion of kurtosis in the valid LRI data for dynamic adjustment, adapting to differences in data centrality. The formula is as follows:

[0219]

[0220] in, Indicates percentile threshold weight. The reliability score represents the percentile threshold. This represents the upper limit of the percentile threshold weight. This is the kurtosis constraint coefficient, which adapts to the tolerance of percentile thresholds to kurtosis. , , The meaning is consistent with the OTSU threshold weight formula;

[0221] The formula for calculating the dynamic proportional threshold weight is as follows:

[0222]

[0223] in, Indicates dynamic proportional threshold weight. The reliability score represents the dynamic scaling threshold.

[0224] The formula for calculating the spatial context adjustment factor weight is as follows:

[0225]

[0226] in, Indicates the spatial context adjustment factor weights;

[0227] The above weights are normalized using the following formula:

[0228]

[0229]

[0230]

[0231]

[0232] in, This represents the normalized OTSU threshold weight. This represents the percentile threshold weight after normalization. This represents the dynamic proportional threshold weight after normalization. This represents the threshold weight of the spatial context adjustment factor after normalization.

[0233] Next, calculate the spatial adjustment factor, which is used to correct the dynamic scaling threshold. This factor, combined with the variability and mean square of the effective LRI data, improves the robustness of the threshold to data fluctuations. The formula is as follows:

[0234]

[0235] in, Indicates the spatial adjustment factor. This represents the dynamic scaling threshold of the maximum LRI value. For spatial adjustment of the reference coefficient, This represents the variance calculation function. This represents the square of the mean. This is the spatial adjustment coefficient. , Preset small positive numbers, ;

[0236] Finally, the adaptive segmentation threshold is calculated. This threshold is obtained by weighted fusion of the OTSU threshold, percentile threshold, dynamic scaling threshold, and spatial adjustment factor, while incorporating range constraints to ensure its reasonableness. The formula is as follows:

[0237]

[0238] in, This represents an adaptive threshold based on data distribution characteristics. This represents the base threshold obtained by the OTSU algorithm. This represents the preset percentile baseline threshold for valid LRI data. This represents the dynamic scaling threshold of the maximum LRI value. Indicates the spatial adjustment factor. This represents the normalized OTSU threshold weight. This represents the percentile threshold weight after normalization. This represents the dynamic proportional threshold weight after normalization. This represents the threshold weight of the spatial context adjustment factor after normalization.

[0239] To ensure the rationality of the adaptive threshold and avoid extreme values ​​from affecting the segmentation effect, a range constraint is applied to the calculated adaptive threshold, and the formula is as follows:

[0240]

[0241] in, This represents the final adaptive threshold after range constraints. The base threshold obtained by the OTSU algorithm, The adaptive threshold is calculated using weighted fusion, with 0.8 and 1.5 being the lower and upper bound constraint coefficients, respectively, ensuring that the adaptive threshold is within 0.8-1.5 times the OTSU threshold.

[0242] To comprehensively evaluate the applicability of various threshold methods, a comprehensive evaluation index system is constructed, taking into account the rationality of the extraction ratio, the appropriateness of the threshold position, and the data separation effect. The formula is as follows:

[0243]

[0244] in, This represents the comprehensive evaluation score of the threshold; a higher value indicates a stronger applicability of the threshold. The score represents the extraction ratio, which assesses the rationality of the landslide extraction area, with a weighting coefficient of 0.3. This represents the threshold position score, which evaluates the relative position of the threshold in the data distribution, with a weighting coefficient of 0.2. This represents the data separation score, which evaluates the effectiveness of the threshold in separating the data, with a weighting coefficient of 0.5.

[0245] Based on the comprehensive evaluation score, the optimal threshold is selected from the candidate threshold set as the final landslide segmentation criterion, and the formula is as follows:

[0246]

[0247] Where represents the optimal segmentation threshold. This indicates taking the parameter corresponding to the maximum value. The threshold for the OTSU algorithm. For dynamic proportional threshold, For an adaptive threshold that has been constrained by range, Indicates threshold The corresponding comprehensive evaluation score;

[0248] The above adaptive threshold calculation method based on data distribution characteristics realizes the adaptive threshold calculation based on LRI spatial distribution characteristics, which can adapt to the data distribution characteristics of different regions and ensure accurate segmentation of landslide areas.

[0249] S6: Landslide Extraction and Result Optimization. The LRI landslide sensitivity index distribution map is shown below. Figure 6 As shown, the landslide extraction results are as follows: Figure 7 As shown.

[0250] The LRI index is binarized based on an adaptive threshold calculated using data distribution characteristics in S5. Pixels above the threshold are marked as landslide candidate areas, and pixels below the threshold are marked as non-landslide areas. Small-area noise is removed through morphological operations (closing followed by opening). The closing operation employs... Elliptical structuring elements are used to fill small holes within a region; the opening operation uses... Elliptical structural elements are used to eliminate isolated noise points.

[0251] First, the LRI index is binarized based on an adaptive threshold, and the formula is as follows:

[0252]

[0253] in, This represents the initial binarization result. Pixels with a value of 1 are identified as potential landslide areas, while pixels with a value of 0 are non-landslide areas.

[0254] Next, morphological optimization is performed on the preliminary extraction results, using a combination of opening and closing operations. Small-area noise and isolated points in the binarized results are removed using morphological opening operations, the formula of which is:

[0255]

[0256] in, This represents the binary image after the opening operation. Represents the morphological opening operator. This indicates a morphological etching operation. This indicates a morphological dilation operation. This represents a 3×3 square structural element. Small-area noise and isolated points are eliminated through a sequence of operations that first erode and then expand, while preserving the shape characteristics of the main landslide area.

[0257] To fill the small holes and broken connection areas in the result after the opening operation, a morphological closing operation is used, with the following formula:

[0258]

[0259] in, This represents the binary image after the closing operation. The morphological closing operator fills small holes and connects fractured areas through a sequence of operations that first expands and then erodes, thereby enhancing the continuity and integrity of the landslide area.

[0260] Through the above optimization steps, high-precision landslide extraction results are finally obtained, including a binarized landslide mask map, optimized boundary information, and a detailed area statistical report, providing reliable data support for landslide disaster assessment.

Claims

1. A landslide extraction method based on multi-source remote sensing data fusion, characterized in that, Includes the following steps: S1: Acquire optical remote sensing images, synthetic aperture radar data, and digital elevation model data of the target area before and after the landslide, and standardize all data to ensure spatial alignment by unifying resolution and projection. S2: Based on the preprocessed optical remote sensing image, calculate the normalized vegetation index change ΔNDVI, where ΔNDVI is the difference between the normalized vegetation index of the first time phase and the normalized vegetation index of the second time phase. The positive value is retained and normalized to obtain the vegetation attenuation factor. Topographic factors are extracted from the preprocessed digital elevation model data. The topographic factors include slope, curvature and topographic roughness. Each topographic factor is normalized. SAR dynamic factors are calculated based on preprocessed synthetic aperture radar data. The SAR dynamic factors include SAR variation index and SAR spatial consistency. The SAR variation index is obtained by weighting the polarization log ratio, polarization ratio change and texture change. The SAR spatial consistency is calculated by the standard deviation of the SAR variation index within a 5×5 window. Each SAR dynamic factor is normalized. S3: The initial weights of slope, curvature and roughness are calculated using the entropy weight method. The slope weight is increased through physical correction to obtain the final terrain factor weights. The weights of the SAR dynamic factors are calculated based on the coefficient of variation. The weight of SAR spatial consistency is the ratio of the sum of its coefficient of variation and the coefficient of variation of the SAR change index. The weight of the SAR change index is the difference between 1 and the ratio. S4: Calculate static terrain risk based on the terrain factors and their weights, calculate SAR dynamic risk based on the SAR dynamic factors and their weights, and construct landslide risk index LRI by combining vegetation attenuation factor. S5: By weighted fusion of OTSU threshold, percentile threshold, dynamic ratio threshold and spatial adjustment factor, and by adding range constraints to ensure reasonableness, an adaptive threshold based on data distribution characteristics is calculated, and the skewness, kurtosis, data density characteristics and spatial context weights of the LRI index of all pixels in the target region are calculated. The basic thresholds were obtained using the OTSU algorithm. The basic threshold was obtained using the percentile method. The basic threshold is obtained using the LRI maximum value dynamic scaling method. The extraction ratio and data density near each basic threshold are calculated to obtain a threshold reliability score. Based on the data distribution characteristics and the threshold reliability score, the weights of the three basic thresholds and the spatial context adjustment factor are dynamically allocated. By weighted fusion of the basic thresholds and the spatial context adjustment factor, combined with range constraints, an adaptive threshold based on the data distribution characteristics is obtained. ; S6: Based on the threshold in S5, the LRI index is binarized. Small area noise and isolated points in the binarization result are removed by morphological opening operation. Small holes and connection fracture areas in the result after opening operation are filled by morphological closing operation to obtain the final landslide extraction result.

2. The landslide extraction method based on multi-source remote sensing data fusion according to claim 1, characterized in that, In S4, the LRI index is calculated using the following formula: in, Indicates static terrain risk factor, This represents the vegetation decay factor, which is the normalized change in the vegetation index. Indicates the dynamic risk factor of SAR; Calculate static terrain risk factors Its formula is: in, , , These represent the final terrain factor weights for slope, curvature, and roughness obtained in step S3, respectively. This represents the normalized slope. This represents the normalized curvature. This represents the normalized terrain roughness. Calculate SAR dynamic risk factors Its formula is: in, This represents the SAR spatial consistency weight obtained in step S3. This represents the SAR change index weights obtained in step S3. This indicates the spatial consistency of the normalized SAR. This represents the normalized SAR change index.

3. The landslide extraction method based on multi-source remote sensing data fusion according to claim 1, characterized in that, In S5, the adaptive threshold calculation method based on data distribution characteristics uses a weighted fusion of the OTSU threshold, percentile threshold, dynamic proportion threshold, and spatial adjustment factor, while incorporating range constraints to ensure rationality. The formula is as follows: in, This represents an adaptive threshold based on data distribution characteristics. This represents the base threshold obtained by the OTSU algorithm. This represents the preset percentile baseline threshold for valid LRI data. This represents the dynamic scaling threshold of the maximum LRI value. Indicates the spatial adjustment factor. This represents the normalized OTSU threshold weight. This represents the percentile threshold weight after normalization. This represents the dynamic proportional threshold weight after normalization. This represents the threshold weight of the spatial context adjustment factor after normalization. First, innovative indicators are constructed to quantify the distribution characteristics and spatial heterogeneity of effective LRI data, providing a basis for threshold optimization. Among them, the data density indicator breaks through the traditional evaluation method that relies on the entire range of data. By using the ratio of interquartile range to data range, it reduces the interference of extreme values ​​and more accurately reflects the data aggregation. Its formula is: in, This represents data density; a larger value indicates that the effective data distribution of LRI is more concentrated. This represents the 75th percentile of the significant data in the LRI. This represents the 25th percentile of the valid data for LRI. This represents the maximum value of valid LRI data. This represents the minimum value of valid LRI data. Indicates a pre-defined small positive number; The spatial context weight is calculated, which breaks through the limitation of traditional thresholds that rely solely on numerical distribution. It combines the dispersion of effective LRI data with the overall level of spatial heterogeneity quantification to reflect the impact of landslide spatial distribution differences on the threshold. The formula is as follows: in, Represents spatial context weights, This represents the set of valid LRI data after removing invalid values. This represents the function for calculating standard deviation. This represents the function for calculating the mean. This is a preset maximum value used to limit the weight range. Preset to small positive numbers; The dynamic scaling threshold for the maximum LRI value is calculated. This threshold breaks away from the traditional fixed scaling design and dynamically adjusts the scaling factor based on the kurtosis of the effective LRI data to adapt to different data distribution characteristics. The formula is as follows: in, This represents the dynamic scaling threshold of the maximum LRI value. This represents the maximum value of valid LRI data. Indicates the dynamic proportional base coefficient. This represents the kurtosis adjustment factor; The kurtosis value represents the effective data of LRI, used to quantify the steepness of the data distribution. This represents the kurtosis constraint coefficient, which prevents excessively large kurtosis from causing abnormal scaling factors. Next, the reliability score for each individual threshold is calculated. This score combines the "reasonableness of the extraction ratio" and the "uniformity of data distribution near the threshold," avoiding the limitations of a single indicator evaluation and providing a basis for dynamic weight allocation. The formula is as follows: in, This represents the reliability score of a single threshold; a higher value indicates a stronger applicability of the threshold. This represents the weighting coefficient of the extracted percentage score. This represents the weighting coefficient of the data density score near the threshold, and , The score represents the extraction ratio, used to assess the rationality of the extracted landslide area. This represents the data density score near the threshold, assessing the uniformity of data distribution; Next, the OTSU threshold weight is calculated. This weight breaks away from the traditional equal weight design and dynamically adjusts the proportion based on the reliability score of the OTSU threshold and the skewness of the valid LRI data. Greater skewness indicates greater data asymmetry, requiring a reduction in the OTSU threshold weight to overcome its limitations. The formula is as follows: in, Indicates the OTSU threshold weight. The reliability score represents the OTSU threshold. The total reliability score is the sum of the reliability scores for the OTSU threshold, percentile threshold, and dynamic proportion threshold, along with the spatial context weights. This represents the skewness value of the valid LRI data. As the lower limit of the weight, This represents the upper limit of the OTSU threshold weight. This is the kurtosis constraint coefficient, which controls the magnitude of the influence of skewness on the weights; Simultaneously, a percentile threshold weight is calculated. This weight combines the reliability score of the percentile threshold with the proportion of kurtosis in the valid LRI data for dynamic adjustment, adapting to differences in data centrality. The formula is as follows: in, Indicates percentile threshold weight. The reliability score represents the percentile threshold. This represents the upper limit of the percentile threshold weight. This is the kurtosis constraint coefficient, which adapts to the percentile threshold's tolerance for kurtosis. , , The meaning is consistent with the OTSU threshold weight formula; The formula for calculating the dynamic proportional threshold weight is as follows: in, Indicates dynamic proportional threshold weight. The reliability score represents the dynamic scaling threshold. The formula for calculating the spatial context adjustment factor weight is as follows: in, Indicates the spatial context adjustment factor weights; The above weights are normalized using the following formula: in, This represents the normalized OTSU threshold weight. This represents the percentile threshold weight after normalization. This represents the dynamic proportional threshold weight after normalization. This represents the threshold weight of the spatial context adjustment factor after normalization. Next, calculate the spatial adjustment factor, which is used to correct the dynamic scaling threshold. This factor, combined with the variability and mean square of the effective LRI data, improves the robustness of the threshold to data fluctuations. The formula is as follows: in, Indicates the spatial adjustment factor. This represents the dynamic scaling threshold of the maximum LRI value. For spatial adjustment of the reference coefficient, This represents the variance calculation function. This represents the square of the mean. This is the spatial adjustment coefficient. It is a preset small positive number.

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