An improved U-Net model-based wide-area InSAR interferogram water body automatic mask method

By improving the U-Net model and using techniques such as overlapping sliding window clipping and distance-weighted average fusion, the problems of low water body extraction accuracy and automation level were solved. This enabled seamless integration of high-precision water body extraction with automated engineering masks, reducing false alarm rate and missed detection rate.

CN122135226APending Publication Date: 2026-06-02HEFEI UNIV OF TECH
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Patent Information

Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
HEFEI UNIV OF TECH
Filing Date
2026-02-11
Publication Date
2026-06-02

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Abstract

This invention provides an automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model, belonging to the field of remote sensing water body extraction technology. The method includes acquiring a remote sensing image to be identified within a target area; inputting the image into a trained U-Net network to obtain a water body information map within the target area; obtaining the water body vector boundary of the target area through the water body information map; using the generated water body vector to mask the water body in the interferometric image; and using the U-Net network to improve the water body feature extraction capability. This invention employs the above-mentioned automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model, which can extract small water body information with high precision and effectively eliminate interference from foreign objects and similar spectral features, extracting complete and accurate water body information, and improving the accuracy and efficiency of interferometric water body masking.
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Description

Technical Field

[0001] This invention relates to the field of remote sensing water body extraction, and in particular to an automatic masking method for wide-area InSAR interferometric images based on an improved U-Net model. Background Technology

[0002] The surface of water bodies in InSAR interferograms can cause severe scattering, leading to decoherence and interfering with deformation monitoring results. Therefore, it is necessary to remove these bodies from the interferogram using a water body mask to improve the accuracy of deformation inversion. When performing water body masking on large-area interferograms, existing water extraction techniques such as single-band thresholding, multi-band interspectral relationship methods (such as NDWI), and traditional machine learning classification methods often suffer from misclassification or omissions due to difficulties in selecting thresholds when faced with complex background interference such as mountain shadows and urban buildings, making it difficult to guarantee accuracy. At the same time, although convolutional neural networks, represented by U-Net, have achieved breakthroughs in image segmentation accuracy, their output raster probability maps cannot be directly adapted to the vector region-based mask analysis process of existing remote sensing engineering software (such as ENVI). This results in the need for cumbersome manual format conversion and manual drawing in actual operations, leading to technical bottlenecks such as data processing chain breaks, low automation, and high labor costs. There is an urgent need for a technical solution that can achieve seamless integration of high-precision extraction and automated engineering masking. Summary of the Invention

[0003] The purpose of this invention is to provide an automatic water body masking method for wide-area InSAR interferometric maps based on an improved U-Net model. This method solves the interface problem between the algorithm model and the application software, significantly improves the accuracy of water body extraction, provides high-quality vector data that meets surveying and mapping standards, and greatly enhances the automation level and operational efficiency of remote sensing image preprocessing and thematic mapping.

[0004] To achieve the above objectives, this invention provides an automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model, comprising the following steps: Step S1: Acquire remote sensing image data to be identified within the target area; Step S2: The image of the target area to be identified is divided into patches according to the cropping rules during training. The patches are input into the pre-trained U-Net neural network model for processing. The U-Net neural network model outputs a water information map of the target area, and each patch is indexed. Step S3: Based on the water body information map, extract and generate the water body vector boundary of the target area; Step S4: Based on the water body vector boundary, use remote sensing image processing software to perform masking processing on the original remote sensing image to obtain image data containing only the water body area.

[0005] Preferably, the remote sensing image to be identified is processed through multiple residual connections to obtain shallow texture features, color features, and deep semantic features; the texture features, color features, and semantic features are then processed by a dilated convolution module to obtain global semantic features and first edge features with a larger receptive field. Simultaneously, the features after residual connection processing of each layer are upsampled to restore the size of the image after residual connection processing and decoded to extract the second edge features; among them, the global semantic features, the first edge features, the texture features, the color features, the semantic features, and the second edge features of each layer are all probability value maps of each pixel belonging to the water body. By using skip connections, global semantic features, first edge features, texture features, color features, semantic features, and second edge features of each layer are sequentially fused to obtain fused features. Water information maps of the target region are obtained by convolution and classification of the fused features.

[0006] Preferably, the total loss function of the U-Net neural network model Binary cross-entropy loss With Dice loss Weighted sum: ; in, This is the balance coefficient; Binary cross-entropy loss : ; In the formula, Total number of pixels Here, represents the binary cross-entropy loss value, and i is the pixel index. For real labels, To predict probabilities; Dice coefficient loss : ; In the formula, This is a smoothing factor used to monitor foreground overlap and prevent the denominator from being zero.

[0007] Preferably, the global semantic features, first edge features, texture features, color features, semantic features, and second edge features of each layer are sequentially fused using skip connections. The water information map of the target region is obtained through convolution and classification of the fused features, specifically including: Based on the spatial index information at the time of cropping, all predicted tiles are reassembled back to the original image size; During the stitching process, a weighted average fusion algorithm is used to process the reserved overlapping areas. That is, the closer the pixel is to the center of the image, the higher the weight is assigned, and the closer it is to the edge, the lower the weight is assigned, so as to eliminate stitching traces and generate a full-size water probability distribution map. To obtain a definite water body distribution range, the full-area water body probability distribution map is binarized, a threshold is set, and pixels larger than the threshold are identified as water bodies. Morphological opening operations are used to remove isolated noise points in the background after binarization, and closing operations are used to fill the holes inside the water bodies, thereby obtaining a water body information map.

[0008] Preferably, based on the water body information map, the water body vector boundary of the target area is extracted and generated, specifically including: Tracing the boundaries of connected regions in a binary mask image of a water body, and transforming these boundaries into vector boundary point sets. ; The Douglas-Peucker algorithm is introduced to perform appropriate smoothing on the vector boundaries formed by the vector boundary point set, within a given threshold. Finding the optimal subset To eliminate grid jagged edges: The final result is a Shapefile (.shp) format vector file with geographic coordinate information, which is the water body vector boundary.

[0009] Preferably, based on the water body vector boundary, the original remote sensing image is masked using remote sensing image processing software to obtain image data containing only the water body area, including the following steps: The water body vector boundary is converted into a Region of Interest (ROI) object. The original image is then filtered using the ROI as a spatial template. The original radiometric or reflectance data of all bands outside the ROI are retained, while the background area of ​​the water body within the ROI is uniformly assigned a NoData value or a specific background value. Finally, an interferogram with the water body removed is output.

[0010] Preferably, the network parameters of the U-Net neural network model are updated using the Adam optimizer. In conjunction with a cosine annealing learning rate decay strategy, the current iteration round learning rate The calculation formula is: ; in, To minimize the learning rate, The initial learning rate, This represents the total number of iterations.

[0011] A remote sensing image water body extraction system, comprising: The image acquisition module is used to acquire and preprocess remote sensing images of the target area; The model inference module contains a pre-trained U-Net network, which is used to receive images and output water body information maps. The vector conversion module is used to convert raster-style water body information maps into vector boundary data. The masking module is used to call remote sensing image processing software interfaces or algorithms to mask images using vector boundaries.

[0012] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method.

[0013] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method.

[0014] Therefore, the present invention employs the above-mentioned automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model, and the technical effects are as follows: The technical solution provided in this application can significantly improve the automation level and extraction accuracy of remote sensing water body monitoring. Compared with the traditional spectral index method, this solution utilizes an improved U-Net fully convolutional neural network and a composite loss function strategy to deeply mine spectral and spatial texture features, effectively solving the problems of difficulty in water body identification under complex backgrounds (such as mountain shadows and urban building interference) and positive and negative sample imbalance, and significantly reducing the false alarm rate and false negative rate.

[0015] By introducing an overlapping sliding window clipping and distance-weighted average fusion algorithm, this application overcomes the limitations of video memory on large-format image processing and completely eliminates the stitching marks and edge effects caused by block prediction, ensuring the continuity of water body distribution.

[0016] This innovative solution establishes an engineering link from deep learning semantic segmentation raster to geographic vector data. By combining morphological optimization and Douglas-Peucker boundary smoothing technology, it achieves automated generation of high-precision vector masks and seamless integration with ENVI software.

[0017] Ultimately, the system directly outputs interference pairs that remove water body interference, greatly reducing the cost of manual interaction and achieving seamless integration of high-precision water extraction and automated engineering masking. Attached Figure Description

[0018] Figure 1 This is a step diagram of an embodiment of this application; Figure 2 This is a diagram of the U-Net network model in the embodiments of this application; Figure 3 This is a diagram showing the water extraction results in an embodiment of this application; Figure 3 (a) represents a real body of water; Figure 3 (b) is the labeled image; Figure 3 (c) The image processed by U-Net; Figure 3 (d) is an image processed using the improved U-Net; Figure 4 This is an image showing the interference pair masking result in an embodiment of this application; Figure 4 (a) is an image of a real water body; Figure 4 (b) Images processed by the improved U-Net; Figure 4 (c) is a vector diagram of the water body in transition; Figure 4 (d) is a mask for interfering with the water body. Detailed Implementation

[0019] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0020] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0021] Example 1 like Figure 1 As shown, an automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model includes the following steps: S1: Acquire remote sensing image data to be identified within the target area; First, high-resolution multispectral remote sensing images of the target monitoring area are selected as the original data source. The data source can be from satellite platforms such as Gaofen-2, Sentinel-2, or Landsat 8. Since the original remote sensing images are inevitably affected by atmospheric scattering, absorption, and surface topography during the imaging process, directly using the original digital quantization values ​​(DN values) for training will lead to a decrease in the model's generalization ability. Therefore, rigorous preprocessing is necessary.

[0022] The specific operational procedure first involves processing the image using the FLAASH atmospheric correction module in ENVI software. The MODTRAN radiative transfer model is then used to eliminate interference from atmospheric water vapor, aerosols, and other factors on the reflectivity of ground features, converting the image's DN values ​​into true surface reflectivity with clear physical meaning. Subsequently, orthorectification is performed on the image based on a high-precision digital elevation model (DEM) of the target area.

[0023] Considering the limitations of deep learning models on input data size and the bottleneck of computer memory capacity, this embodiment adopts a sliding window cropping strategy. Assume the preprocessed original image is... The cutting size is set to (For example To avoid edge artifacts (pixels), an overlap strategy is introduced. The overlap rate is set to... (In this embodiment, the value is 20% to 25%), so the step size of the sliding window is (Stride). The calculation is as follows: ); The image is cropped into a set of tiles using this step size. At the same time, construct the corresponding binary label map. Water bodies are labeled as 1, and the background is labeled as 0. An online data augmentation mechanism is introduced during the training iteration process. The input image is randomly rotated, flipped, and Gaussian noise is added. The calculation formula is as follows: ; in, To randomly enhance parameters, thereby increasing sample diversity.

[0024] S2: Input the remote sensing image to be identified into a pre-trained U-Net neural network model for processing; like Figure 2 , Figure 2 This is a U-Net network model for a SAR water masking method based on the U-Net model in an embodiment of this application.

[0025] In constructing the core recognition model, this embodiment adopts an improved U-Net fully convolutional neural network architecture. This network exhibits a classic "U"-shaped symmetrical structure, mainly composed of a contraction path (encoder) on the left and an expansion path (decoder) on the right. The contraction path is primarily responsible for image feature extraction and compression, consisting of four consecutive convolutional modules. Each module contains two 3×3 convolutional layers and a 2×2 max-pooling layer. ReLU activation functions are applied after the convolutional layers to introduce non-linear features. As the network depth increases, the spatial resolution of the image gradually decreases, but the number of feature channels gradually increases, thus enabling the gradual abstraction of deep semantic features from shallow texture and color features. The expansion path is mainly responsible for restoring the spatial resolution of the feature map to the original input size. It gradually enlarges the feature map through upsampling operations and uses a skip connection structure to concatenate the high-resolution feature maps of corresponding layers in the contraction path with the upsampled feature maps in the expansion path. This design is crucial because it can directly pass the rich spatial details (such as the edge contours of water bodies and the textures of small tributaries) preserved in the encoder to the decoder, effectively solving the problem that deep networks are prone to losing edge details during upsampling, thus achieving end-to-end pixel-level accurate classification.

[0026] The shrinking path (encoder) is responsible for feature extraction and compression. Let the first... The input of the layer encoder is The output is Its operation involves two steps. Convolution, ReLU activation, and Max pooling, mathematically expressed as: ; in, express Max pooling, express convolution, This represents the ReLU activation function. As the number of layers increases, the spatial resolution of the feature map decreases, while the number of channels increases.

[0027] The expansion path (decoder) is responsible for resolution restoration. It progressively enlarges the feature map using upsampling operations and fuses features through skip connections. Let the... The input to the layer decoder is The corresponding encoder features are Then output The calculation is as follows: ; in, For upsampling operations, Concat[•] denotes concatenation along the channel dimension. This design allows the rich spatial details to be directly passed to the decoder, achieving end-to-end pixel-level accurate classification.

[0028] S3: Output a water body information map within the target area using the U-Net neural network model; The model training process employs a composite loss function strategy combining the Binary Cross Entropy Loss and the Dice Loss. Given that water pixels often constitute only a small portion of remote sensing images, resulting in severe sample imbalance, the Dice loss function focuses more on the overlap of foreground targets (water bodies), effectively mitigating the problem of class imbalance causing the model to tend to predict the background. The Adam optimizer is used to iteratively update the network parameters, with an initial learning rate set to 0.0001, coupled with a cosine annealing learning rate decay strategy. This allows for rapid convergence in the early stages of training, followed by fine-tuning of parameters in later stages to find the global optimum. The training process is set to 100 iterations, during which the loss value on the validation set is monitored in real time, and the model weight file with the lowest loss value on the validation set is saved as the final inference model.

[0029] Given the imbalance in the distribution of water samples in remote sensing images, a total loss function is defined. Binary cross-entropy loss With Dice loss Weighted sum: ; in, This is the balance coefficient.

[0030] Binary cross-entropy loss ( ): ; In the formula, Total number of pixels Here, represents the binary cross-entropy loss value, and i is the pixel index. For real labels, To predict probabilities.

[0031] Dice coefficient loss : ; In the formula, Smoothing factor (take) ), used to focus on foreground overlap and prevent the denominator from being zero.

[0032] Update network parameters using the Adam optimizer This is combined with a cosine annealing learning rate decay strategy. Current iteration round. learning rate The calculation formula is: ; in, To minimize the learning rate, The initial learning rate, This represents the total number of iterations.

[0033] After obtaining the trained U-Net model, the inference and water body information map generation stages begin. The image of the target region to be identified is segmented into patches according to the cropping rules during training and input into the model. The model outputs a probability value map of each pixel belonging to water. Subsequently, all predicted patches are re-stitched back to the original image size based on the spatial index information during cropping. During the stitching process, a weighted average fusion algorithm is used to process the reserved overlapping areas, that is, pixels closer to the image center are given higher weights, and pixels closer to the edge are given lower weights, thereby eliminating stitching marks and generating a full-area water body probability distribution map. To obtain a definite water body distribution range, the probability map needs to be binarized. Usually, 0.5 is selected as the threshold, and pixels greater than this threshold are identified as water. However, the result of direct binarization often contains noise or small holes. Therefore, this embodiment further employs morphological post-processing techniques, using morphological opening operations to remove isolated noise in the background and using closing operations to fill holes inside the water body, thereby obtaining a high-precision water body binary mask map with smooth edges and good internal connectivity, such as... Figure 3 As shown.

[0034] Let pixels exist The predicted probabilities in the overlapping patches are respectively The corresponding spatial distance weight is (The closer to the center, the higher the weight), then the final probability after fusion for: ; To obtain a definite water body distribution, the probability map is binarized, and a threshold is applied. : ; This represents the image after binarization.

[0035] Subsequently, morphological opening operations are used to remove noise, and closing operations are used to fill the holes. ; in, As a structural element, The final output is a deformed binary image. The original binary image to be processed. For the opening operator, It is a closing operator.

[0036] S4: Based on the water body information map, extract and generate the water body vector boundary of the target area; To achieve seamless integration with professional remote sensing software such as ENVI, this embodiment details the conversion process from raster data to vector data and the masking application process. Using polygonization functions from the GDAL library or contour extraction algorithms from OpenCV, the boundaries of connected regions in the binary water map are traced and converted into vector polygon data. To avoid jagged edges during the raster-to-vector conversion, the Douglas-Peucker algorithm is introduced to moderately smooth the vector boundaries, reducing redundant nodes while preserving the geometric features of the boundaries, ultimately generating a Shapefile (.shp) format vector file with geographic coordinate information.

[0037] Tracing using GDAL / OpenCV The boundary of the connected region is transformed into a set of vector points. The Douglas-Peucker algorithm is introduced to smooth vector boundaries, within a given threshold. Finding the optimal subset To eliminate grid jagged edges: .

[0038] S5: Based on the water body vector boundary, use remote sensing image processing software (such as ENVI) to perform masking processing on the original remote sensing image to obtain image data containing only the water body area.

[0039] To achieve the mapping from geometric boundaries to entity spectral data, an automated script was written to call the functional interfaces of the ENVI software (such as the IDL Task API). First, a smoothed Shapefile vector file with geographic coordinate information and the original multispectral remote sensing image were loaded into the software platform. The system automatically converted the vector polygons into ENVI-specific Region of Interest (ROI) objects, ensuring precise alignment within the same geographic reference frame. Subsequently, a masking or ROI-based subset operation was performed, using the water body ROI as a spatial template to filter the original image. During this process, the algorithm retained the original radiance or reflectance data for all bands outside the ROI, while uniformly assigning the water body background area within the ROI a value of NoData or a specific background value (such as 0). The final output is an interferogram with the water body removed. This image fully preserves the interferometric results excluding the water body and can be directly used as high-quality basic data for settlement monitoring in the area, achieving a seamless conversion of deep learning recognition results to InSAR products.

[0040] The final generated Shapefile (.shp) file is loaded into ENVI via an automated script. The script drives ENVI to perform a masking operation, using the ROI as a template to mask the original interference pattern. The process is performed to generate a water mask interference pattern. : ; This step transforms the semantic segmentation results from deep learning into entity data that conforms to surveying and remote sensing analysis standards, ultimately outputting a water body mask interferogram, such as... Figure 4 As shown.

[0041] Therefore, the present invention adopts the above-mentioned automatic water body masking method for wide-area InSAR interferometric maps based on the improved U-Net model, which solves the interface problem between the algorithm model and the application software, significantly improves the accuracy of water body extraction, provides high-quality vector data that meets surveying and mapping standards, and greatly improves the automation level and operational efficiency of remote sensing image preprocessing and thematic mapping.

[0042] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for automatic water body masking in wide-area InSAR interferometric images based on an improved U-Net model, characterized in that, Includes the following steps: Step S1: Acquire remote sensing image data to be identified within the target area; Step S2: The image of the target area to be identified is divided into patches according to the cropping rules during training. The patches are input into the pre-trained U-Net neural network model for processing. The U-Net neural network model outputs a water information map of the target area, and each patch is indexed. Step S3: Based on the water body information map, extract and generate the water body vector boundary of the target area; Step S4: Based on the water body vector boundary, use remote sensing image processing software to perform masking processing on the original remote sensing image to obtain image data containing only the water body area.

2. The automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model according to claim 1, characterized in that, The remote sensing image to be identified is processed through multiple residual connections to obtain shallow texture features, color features, and deep semantic features. The texture features, color features, and semantic features are then processed by a dilated convolution module to obtain global semantic features and first edge features with a larger receptive field. Simultaneously, the features after residual connection processing of each layer are upsampled to restore the size of the image after residual connection processing and decoded to extract the second edge features; among them, the global semantic features, the first edge features, the texture features, the color features, the semantic features, and the second edge features of each layer are all probability value maps of each pixel belonging to the water body. By using skip connections, global semantic features, first edge features, texture features, color features, semantic features, and second edge features of each layer are sequentially fused to obtain fused features. Water information maps of the target region are obtained by convolution and classification of the fused features.

3. The automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model according to claim 1, characterized in that, The total loss function of the U-Net neural network model Binary cross-entropy loss With Dice loss Weighted sum: ; in, This is the balance coefficient; Binary cross-entropy loss : ; In the formula, Total number of pixels Here, represents the binary cross-entropy loss value, and i is the pixel index. For real labels, To predict probabilities; Dice coefficient loss : ; In the formula, This is a smoothing factor used to monitor foreground overlap and prevent the denominator from being zero.

4. The automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model according to claim 2, characterized in that, The global semantic features, first edge features, texture features, color features, semantic features, and second edge features of each layer are sequentially fused using skip connections. The fused features are then convolved and classified to obtain a water body information map of the target region, specifically including: Based on the spatial index information at the time of cropping, all predicted tiles are re-stitched back to the original image size; During the stitching process, a weighted average fusion algorithm is used to process the reserved overlapping areas. That is, the closer the pixel is to the center of the image, the higher the weight is assigned, and the closer it is to the edge, the lower the weight is assigned, so as to eliminate stitching traces and generate a full-size water probability distribution map. To obtain a definite water body distribution range, the full-area water body probability distribution map is binarized, a threshold is set, and pixels larger than the threshold are identified as water bodies. Morphological opening operations are used to remove isolated noise points in the background after binarization, and closing operations are used to fill the holes inside the water bodies, thereby obtaining a water body information map.

5. The automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model according to claim 1, characterized in that, Based on the water body information map, the water body vector boundary of the target area is extracted and generated, specifically including: Tracing the boundaries of connected regions in a binary mask image of a water body, and transforming these boundaries into vector boundary point sets. ; The Douglas-Peucker algorithm is introduced to perform appropriate smoothing on the vector boundaries formed by the vector boundary point set, within a given threshold. Finding the optimal subset To eliminate grid jagged edges: The final result is a Shapefile (.shp) format vector file with geographic coordinate information, which is the water body vector boundary.

6. The automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model according to claim 1, characterized in that, Based on the water body vector boundary, the original remote sensing image is masked using remote sensing image processing software to obtain image data containing only the water body region, including the following steps: The water body vector boundary is converted into a Region of Interest (ROI) object. The original image is then filtered using the ROI as a spatial template. The original radiometric or reflectance data of all bands outside the ROI are retained, while the background area of ​​the water body within the ROI is uniformly assigned a NoData value or a specific background value. Finally, an interferogram with the water body removed is output.

7. The automatic water body masking method for wide-area InSAR interferometric images based on an improved U-Net model according to claim 1, characterized in that, Update network parameters of the U-Net neural network model using the Adam optimizer In conjunction with a cosine annealing learning rate decay strategy, the current iteration round learning rate The calculation formula is: ; in, To minimize the learning rate, The initial learning rate, This represents the total number of iterations.

8. A remote sensing image water body extraction system for implementing the method of any one of claims 1 to 7, characterized in that, include: The image acquisition module is used to acquire and preprocess remote sensing images of the target area; The model inference module contains a pre-trained U-Net network, which is used to receive images and output water body information maps. The vector conversion module is used to convert raster-style water body information maps into vector boundary data. The masking module is used to call remote sensing image processing software interfaces or algorithms to mask images using vector boundaries.

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

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 7.