River section scale low-altitude sediment particle size measuring method and device

Abstract

This invention discloses a method and apparatus for low-altitude measurement of sediment particle size at the river section scale. The method includes: multi-scale compression of UAV orthophotos at the river section scale; recursive slicing of the image at each scale based on memory usage estimation to obtain multiple image slices at each scale; inputting each image slice and different image compression coefficients into a sediment particle recognition model to obtain sediment particle recognition results for each image slice; mapping the sediment particle recognition results of all image slices to the original image coordinate system to determine cross-scale occupancy areas; fusing sediment particle instances in the cross-scale occupancy areas; combining the fused sediment particle instances in the cross-scale occupancy areas with those in non-cross-scale occupancy areas to obtain multi-scale fused sediment particle instance data; and obtaining the sediment particle size distribution based on the sediment particle instance data. This invention enables rapid and accurate measurement of sediment particle size at the river section scale.

Description

Technical Field

[0001] The embodiments of this invention relate to the fields of artificial intelligence security, trusted computing, intelligent agent control, and automated system security technology, and particularly to a method, device, and system for low-altitude measurement of sediment particle size at the river section scale. Background Technology

[0002] Image-based sediment particle size measurement technology has developed rapidly in recent years. However, due to the limited range of image acquisition, field applications mainly rely on handheld cameras or drones to take single-point photos for local sampling. The spatial scale and particle size range of the measurement are small, and the obtained sediment particle size distribution cannot reflect the spatial heterogeneity of river sediment. Currently, there is a lack of technology for rapid measurement of riverbed sediment particle size at the field river scale. The main difficulties are: (1) The particle size distribution of sediment in natural river channels varies greatly, and single-scale AI image recognition models are difficult to accurately identify particles of different sizes; (2) The amount of drone image data at the river scale is huge, and direct application of AI models is likely to exceed the hardware memory limit, making it difficult to achieve continuous and efficient processing of large-scale images with limited computing power.

[0003] The background section described above is merely a description made by the inventor based on his understanding, and the above content should not be regarded as evidence of prior art disclosed before the filing date of this application. Summary of the Invention

[0004] This invention provides a low-altitude measurement method for sediment particle size at the river section scale, enabling rapid and accurate measurement of sediment particle size at the river section scale, including: By presetting multiple different image compression coefficients, multi-scale compression is performed on the orthophotos of the UAV at the river section scale to obtain images at multiple scales. Recursively slice the image at each scale based on the estimated video memory usage to obtain multiple image slices at each scale. Each image slice and its corresponding image compression coefficient are input into the sediment particle recognition model to obtain the sediment particle recognition result for each image slice. The sediment particle recognition model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. After mapping the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, the cross-scale occupancy area is determined. Based on the occupancy degree of sediment particle instances in the cross-scale occupancy area, the sediment particle instances in the cross-scale occupancy area are fused. Combining the fused sediment particle instances in the cross-scale occupancy area and the sediment particle instances in the non-cross-scale occupancy area, the multi-scale fused sediment particle instance data is obtained. Based on the sample data of sediment particles, the particle size distribution of sediment was obtained.

[0005] Another aspect of the present invention provides a low-altitude measurement device for sediment particle size at the river section scale, for achieving rapid and accurate measurement of sediment particle size at the river section scale, comprising: The multi-scale compression module is used to perform multi-scale compression on UAV orthophotos at the river section scale by presetting multiple different image compression coefficients to obtain images at multiple scales. The slicing module is used to recursively slice the image at each scale based on the estimated video memory usage, resulting in multiple image slices at each scale. The identification module is used to input each image slice and its corresponding image compression coefficient into the sediment particle identification model to obtain the sediment particle identification result for each image slice. The sediment particle identification model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. The fusion module is used to map the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, determine the cross-scale occupied area, and based on the occupancy degree of sediment particle instances in the cross-scale occupied area, fuse the sediment particle instances in the cross-scale occupied area, and combine the fused sediment particle instances in the cross-scale occupied area and the sediment particle instances in the non-cross-scale occupied area to obtain multi-scale fused sediment particle instance data. The particle size measurement module is used to obtain the particle size distribution of sediment based on sample data of sediment particles.

[0006] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned method for low-altitude measurement of sediment particle size at the river section scale.

[0007] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for low-altitude measurement of sediment particle size at the river section scale.

[0008] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-mentioned method for low-altitude measurement of sediment particle size at the river section scale.

[0009] In this embodiment of the invention, multiple different image compression coefficients are preset to perform multi-scale compression on UAV orthophotos at the river section scale, resulting in images at multiple scales. Recursive slicing based on memory usage estimation is performed on each scale image to obtain multiple image slices at each scale. Each image slice and its corresponding image compression coefficient are input into a sediment particle recognition model to obtain sediment particle recognition results for each image slice. The sediment particle recognition model is trained using historical UAV orthophotos at the river section scale on a deep learning-based instance segmentation model. After mapping the sediment particle recognition results of all image slices to the original image coordinate system of the UAV orthophotos, cross-scale occupancy areas are determined. Based on the occupancy degree of sediment particle instances within the cross-scale occupancy areas, the sediment particle instances in the cross-scale occupancy areas are fused. Combining the fused sediment particle instances in the cross-scale occupancy areas with those in non-cross-scale occupancy areas, multi-scale fused sediment particle instance data is obtained. The sediment particle size distribution is obtained based on the sediment particle instance data. By pre-setting multiple different image compression coefficients, multi-scale compression is performed on UAV orthophotos at the river section scale, resulting in images of multiple scales. This allows the same image to exhibit different particle size scales under different compression coefficients, providing a multi-resolution information foundation for subsequent identification. The data volume of the compressed low-scale images is significantly reduced, avoiding the computational resource pressure caused by directly processing ultra-high-resolution orthophotos. The memory usage of image slices is calculated, and automatic recursive segmentation is performed when the memory usage exceeds the limit, ensuring the stable operation of the subsequent sediment particle identification model under limited memory, without the need for manual pre-setting of slice sizes. Within the allowable memory range, the slice size is retained as large as possible to reduce the number of slices, thereby reducing redundant calculations caused by slice overlap and the complexity of subsequent fusion. The image compression coefficient is used as explicit conditional information input to the sediment particle identification model, allowing the model to know which compression scale the currently processed image slice comes from, thus adopting an appropriate identification strategy at different scales and improving the accuracy and consistency of cross-scale identification. In high-compression (low-resolution) images, sediment particle identification models focus on large-scale structural features; in low-compression (high-resolution) images, they retain sensitivity to small sediment particles. Combining these two approaches allows the sediment particle identification model to simultaneously cover a wide particle size range. The same particle may be identified in images at different scales, and direct stitching would lead to duplicate counting. By using cross-scale occupancy region detection and fusion based on occupancy degree, it is possible to accurately determine which sediment particle instances represent the same physical particle, avoiding duplication or omission. The fusion strategy based on occupancy degree allows the scale results with higher confidence and clearer boundaries to dominate the fusion process, thereby improving the quality of the final particle instance data. The fused sediment particle instance data integrates the advantages of each scale, including the overall morphology of large sediment particles while preserving the fine boundaries of small sediment particles, forming complete information on particle distribution at the river section scale. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a flowchart of low-altitude measurement of sediment particle size at the river section scale in an embodiment of the present invention; Figure 2 This is a schematic diagram of an orthophoto of a UAV in an embodiment of the present invention; Figure 3 This is a schematic diagram of image slicing in an embodiment of the present invention; Figure 4 This is a schematic diagram of the mud and sand particle identification results for each slice in an embodiment of the present invention; Figure 5 This is a schematic diagram of the low-altitude measurement device for sediment particle size at the river section scale in an embodiment of the present invention. Figure 6 This is a schematic diagram of a computer device in an embodiment of the present invention. Detailed Implementation

[0011] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. Here, the illustrative embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0012] Figure 1 This is a flowchart of the low-altitude measurement method for sediment particle size at the river section scale in an embodiment of the present invention, as shown below. Figure 1 As shown, it includes: Step 101: By presetting multiple different image compression coefficients, multi-scale compression is performed on the UAV orthophoto at the river section scale to obtain images at multiple scales. Step 102: Perform recursive slicing on the image at each scale based on the estimated video memory usage to obtain multiple image slices at each scale. Step 103: Input each image slice and its corresponding image compression coefficient into the sediment particle recognition model to obtain the sediment particle recognition result for each image slice. The sediment particle recognition model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. Step 104: After mapping the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, determine the cross-scale occupied area. Based on the occupancy degree of sediment particle instances in the cross-scale occupied area, fuse the sediment particle instances in the cross-scale occupied area. Combine the fused sediment particle instances in the cross-scale occupied area with the sediment particle instances in the non-cross-scale occupied area to obtain multi-scale fused sediment particle instance data. Step 105: Obtain the particle size distribution of sediment based on the sample data of sediment particles.

[0013] Depend on Figure 1 As shown in the flowchart, in this embodiment of the invention, multiple different image compression coefficients are preset to perform multi-scale compression on UAV orthophotos at the river section scale, resulting in images of multiple scales. This allows the same image to exhibit different particle size scales under different compression coefficients, providing a multi-resolution information basis for subsequent recognition. The amount of low-scale image data after compression is significantly reduced, avoiding the computational resource pressure caused by directly processing ultra-high-resolution orthophotos. The memory usage of image slices is calculated, and automatic recursive segmentation is performed when the memory usage exceeds the memory limit, ensuring that the subsequent sediment particle recognition model runs stably under limited memory, without the need for manual preset slice sizes. Within the allowable memory range, larger slice sizes are retained as much as possible to reduce the number of slices, thereby reducing redundant calculations caused by overlapping slices and the complexity of subsequent fusion. The image compression coefficient is input as explicit conditional information into the sediment particle recognition model, allowing the model to know which compression scale the currently processed image slice comes from, thus adopting an appropriate recognition strategy at different scales and improving the accuracy and consistency of cross-scale recognition. In high-compression (low-resolution) images, sediment particle identification models focus on large-scale structural features; in low-compression (high-resolution) images, they retain sensitivity to small sediment particles. Combining these two approaches allows the sediment particle identification model to simultaneously cover a wide particle size range. The same particle may be identified in images at different scales, and direct stitching would lead to duplicate counting. By using cross-scale occupancy region detection and fusion based on occupancy degree, it is possible to accurately determine which sediment particle instances represent the same physical particle, avoiding duplication or omission. The fusion strategy based on occupancy degree allows the scale results with higher confidence and clearer boundaries to dominate the fusion process, thereby improving the quality of the final particle instance data. The fused sediment particle instance data integrates the advantages of each scale, including the overall morphology of large sediment particles while preserving the fine boundaries of small sediment particles, forming complete information on particle distribution at the river section scale.

[0014] In step 101, by presetting multiple different image compression coefficients, the UAV orthophoto at the river section scale is compressed at multiple scales to obtain images at multiple scales. This invention's embodiments utilize high-resolution UAV cameras to acquire orthophotos of river sections using UAV cameras. Figure 2 This is a schematic diagram of an orthophoto taken by a UAV in an embodiment of the present invention. The particle size range of wide-graded riverbed sediment can be two to three orders of magnitude, ranging from centimeters to meters. In a single-resolution UAV orthophoto, large sediment particles occupy a large amount of pixel space, while small sediment particles are compressed to only a few pixels, resulting in extremely poor detection performance of traditional artificial intelligence recognition models for wide-graded sediment particles.

[0015] By actively compressing UAV orthophotos with different coefficients—a process known as downsampling—a multi-scale image series is constructed. In low-resolution (high-compression) images, the area proportion of large sediment particles decreases to the optimal range for sediment particle recognition models; in high-resolution (low-compression) or original-resolution images, small sediment particles retain sufficient pixel detail. This ensures that each size of sediment particle has an image scale most suitable for its dimensions.

[0016] First, determine the image compression coefficient set. Based on the prior particle size distribution information of sediment in the river section, pre-set the image compression coefficient set C to be equal to {c1, c2, ..., c...}. k The image compression factor is defined as the compressed size divided by the original size, and its value ranges from greater than 0 to less than or equal to 1. When the image compression factor is equal to 1, it means that the original resolution is not compressed. The smaller the image compression factor, the higher the degree of compression and the lower the image resolution.

[0017] The image compression factor preset strategy is as follows: For large mud and sand particles in the meter range, it is recommended that the image compression factor be between 0.1 and 0.2, using high compression to reduce the area of ​​large mud and sand particles to the optimal recognition range; for medium mud and sand particles in the decimeter range, it is recommended that the image compression factor be between 0.3 and 0.5, using medium compression; for small mud and sand particles in the centimeter range, it is recommended that the image compression factor be between 0.8 and 1.0, using low compression or maintaining the original resolution to preserve details.

[0018] For example, for typical wide-graded sediment in riverbeds, with particle sizes ranging from two centimeters to two meters, three image compression coefficients are preset: 0.15 for large sediment particles, 0.4 for medium sediment particles, and 1.0 for small sediment particles.

[0019] The UAV orthophotos are downsampled using each value in the compression factor set to generate a multi-scale image series.

[0020] The following downsampling methods can be selected: Bilinear interpolation is suitable for general scenarios and has the advantage of smooth anti-aliasing; Bicubic interpolation is suitable for scenarios that need to preserve texture, and has good detail preservation but large computational cost; Nearest neighbor interpolation is suitable for scenarios that need to maintain the original pixel value distribution, is fast and does not introduce new pixel values ​​but has obvious jagged edges.

[0021] In addition, the information entropy of the compressed image can be calculated to ensure that it is not lower than a preset threshold such as 60% of the original entropy; the pixel diameter of the smallest mud and sand particle in the compressed image, i.e., the lower limit of the target magnitude, can be checked to ensure that it is not lower than the minimum number of pixels that the mud and sand particle recognition model can effectively recognize, for example, not less than 5×5 pixels.

[0022] If the compressed image does not meet the above conditions, adjust the set of compression coefficients and re-perform compression.

[0023] In step 102, recursive slicing is performed on the image at each scale based on the estimated video memory usage, resulting in multiple image slices at each scale. In one embodiment, recursive slicing based on memory usage estimation is performed on the image at each scale to obtain multiple image slices at each scale, including: For each scale of the image, image slices are divided according to the reference slice size, and the overlapping area between adjacent image slices is maintained by a preset overlap rate; For image slices whose boundaries are smaller than the reference slice size, mirror filling is used to expand them to the reference slice size, generating a slice queue containing all image slices; For each image slice in the slice queue, the video memory usage is calculated based on the size and content complexity of the image slice. If the video memory usage is greater than the video memory usage threshold, the image slice is recursively segmented using a new baseline slice size until the video memory usage of each image slice after segmentation is less than or equal to the video memory usage threshold, or the size of each image slice after segmentation reaches the lower bound of the size.

[0024] In the above embodiments, for each scale of the image, it is first divided into grids according to a preset reference slice size to achieve image slice segmentation. The reference slice size is set based on the recommended video memory capacity of the target GPU and the single video memory overhead of the mud and sand particle recognition model inference. It is usually set to a larger size that the mud and sand particle recognition model can stably process in order to maximize processing efficiency.

[0025] Adjacent image slices maintain an overlap area with a preset overlap rate. The overlap rate is typically set between 10% and 30%. The purpose of setting the overlap area is that when a sediment particle is cut off by the slice boundary, the sediment particle will appear partially in both adjacent slices. Subsequent fusion algorithms can merge these fragmented identification results into a complete sediment particle instance, thereby avoiding the missed detection or incomplete identification of sediment particles at the boundary.

[0026] For areas at the image boundary that are smaller than the reference slice size, instead of directly discarding or zero-filling, they are expanded to the reference slice size using mirror filling.

[0027] The specific operation of mirror fill is as follows: using the image boundary as a mirror, the pixels inside the boundary are symmetrically reflected to the outer area, thereby expanding the insufficient area to the full slice size. For example, when the right edge of the image slice is not far from the right boundary of the image, the pixels inside the image that are close to the boundary are mirror-symmetrically copied using the right boundary of the image as an axis to fill the missing area on the right.

[0028] Compared to discarding, mirror fill preserves complete information of the edge region. Compared to zero fill, it avoids introducing black or white pixels unrelated to riverbed sediment at the edges, thus preventing AI models from misidentifying the filled area as background or anomalies. After mirror fill processing, all boundary regions are expanded to a uniform baseline slice size, forming a complete slice queue.

[0029] For each image slice in the slice queue, a preliminary estimate of video memory usage is performed. The video memory usage is not simply the number of pixels multiplied by a fixed coefficient, but rather takes into account the slice size and content complexity.

[0030] Content complexity can be represented using image information entropy. Higher image entropy indicates richer texture and denser sediment particles in the image slice. This increases the size and computational cost of the intermediate feature map for the sediment particle recognition model on that slice, leading to higher memory usage. Specifically, memory usage M_est consists of three parts: fixed model overhead M_base, base memory usage proportional to pixel area, and incremental memory usage proportional to content complexity. Fixed model overhead includes the fixed usage of model parameters and optimizer states during inference. Base memory usage is proportional to the product of the slice's width and height, while incremental memory usage is proportional to the image slice's information entropy.

[0031] The formula for calculating video memory usage M_est is as follows: M_est = M_base + α × (w × h) + β × H(tile) Where M_est represents the GPU memory usage, measured in MB or GB, and M_base represents the model's fixed overhead, including the amount of GPU memory used during inference for model parameter weights, optimizer states, CUDA kernel context, etc. This value can be measured through a single unloaded inference test and is constant for a given model and hardware platform. For example, for a segmentation model, M_base is typically between 500 MB and 1.5 GB.

[0032] α × (w × h): Basic pixel memory usage. Where w is the width of the image slice, h is the height of the image slice, and w multiplied by h is the total number of pixels in the image slice. α is the memory usage coefficient per unit pixel. This coefficient reflects the memory usage of the feature maps generated by the input image in each layer of the network model, and its value is related to the network depth and number of channels. For typical segmentation models, the value of α ranges from approximately 0.5 to 2.0.

[0033] β × H(tile): Content complexity increment. H(tile) is the information entropy of the image tile, used to quantify the complexity of the image content. The formula for calculating information entropy is H(tile) = -Σ p(i) × log2 p(i), where p(i) is the probability of pixel grayscale value i appearing. A larger information entropy indicates richer image texture and denser sediment particles, resulting in sparser or denser activation values ​​in the intermediate feature maps generated by the model on that tile, thus causing fluctuations in memory usage. β is the content complexity coefficient, which needs to be calibrated experimentally; a typical value range is 5 to 20.

[0034] The calculated memory usage M_est is compared with the preset memory usage threshold θ_oom. The memory usage threshold is usually set to 80% to 90% of the target GPU's physical memory capacity, reserving some memory space for system overhead and burst memory spikes.

[0035] If the video memory usage M_est is less than or equal to the video memory usage threshold θ_oom, then the image slice is determined to be safe to process on the current GPU and sent to the subsequent recognition process.

[0036] If the estimated memory usage M_est is greater than the memory usage threshold θ_oom, recursive segmentation is triggered. At this point, a new reference slice size is used to segment the image slice. This new reference slice size is typically half the current slice size, dividing the current slice into four sub-image slices in a 2×2 grid, or it can be divided horizontally or vertically based on the image's aspect ratio. Each sub-image slice inherits the original overlap ratio setting, meaning that the overlap area between sub-image slices and with adjacent image slices remains the same. The generated sub-image slices are appended to the tail of the processing queue, marked with their parent slice ID and current segmentation depth, awaiting further processing.

[0037] The recursive segmentation process continues. After each segmentation, the memory usage of the newly generated sub-image slice is recalculated and compared with the memory usage threshold again. The recursive process terminates when one of the following two conditions is met.

[0038] The first termination condition is: the memory usage of the current sub-image slice is less than or equal to the memory usage threshold. In this case, the sub-image slice can be safely sent to the GPU for processing.

[0039] The second termination condition is when the size of the current sub-image slice reaches the preset lower bound of the slice scale. The lower bound of the slice scale is a minimum slice size preset based on the accuracy requirements of mud and sand particle recognition. When the slice size is too small, a complete mud and sand particle may be cut into multiple slices, seriously affecting the accuracy of subsequent mud and sand particle matching and fusion. Therefore, even if the estimated video memory usage still exceeds the video memory usage threshold, segmentation will not continue, but the slice will be marked and proceed to subsequent steps.

[0040] Figure 3 This is a schematic diagram of an image slice in an embodiment of the present invention. As can be seen, the image slice can display the sediment particles more clearly compared to the original image.

[0041] Furthermore, when the slice size reaches its lower bound and the estimated GPU memory usage still exceeds the GPU memory usage threshold, the slice is marked as an ultra-large dense region. At this point, further segmentation is stopped, and instead, a computing device switching approach is used: the pixel data of the image slice is released from GPU memory, copied to host memory, and then the CPU version of the recognition model is invoked for inference. Although CPU inference is slower, it ensures processing stability and avoids program crashes due to GPU memory overflow. After CPU inference is completed, the recognition results are appended with metadata tags for reference in subsequent fusion steps.

[0042] In step 103, each image slice and its corresponding image compression coefficient are input into the sediment particle recognition model to obtain the sediment particle recognition result for each image slice. The sediment particle recognition model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. In one embodiment, the sediment particle identification model includes: A multi-scale feature encoder is used to generate a multi-scale feature pyramid from input image slices. The multi-scale feature pyramid includes multiple feature maps with different resolutions and semantics. The scale-aware feature modulator is used to linearly modulate the two feature maps with the most semantic representation ability in the multi-scale feature pyramid based on the image compression coefficients corresponding to the input image slices, and then replaces the two feature maps with the most semantic representation ability in the multi-scale feature pyramid with the modulated two feature maps. The particle adhesion decoupling head is used to predict the pixel-level segmentation mask, the adhesion probability between particles, and the offset vector of each pixel pointing to the center of its respective particle from the current multi-scale feature pyramid, and obtain the binary segmentation mask, adhesion probability map and center offset vector field respectively. An instance assembler is used to obtain the mud and sand particle identification results of the input image slice based on the binary segmentation mask, the adhesion probability map and the center offset vector field. The mud and sand particle identification results include the binary segmentation mask and the identification scale label for each mud and sand particle instance.

[0043] In the above embodiments, the multi-scale feature encoder is the fundamental backbone module of the sediment particle recognition model. Its function is to convert the input image slices into a multi-scale feature pyramid. The multi-scale feature encoder receives a single image slice as input, typically a three-channel RGB color image with a preset slice size. The output of the multi-scale feature encoder is a multi-scale feature pyramid, which contains feature maps with multiple different resolutions and semantic abstraction levels.

[0044] The structure of the feature pyramid: At the bottom of the feature pyramid, the high-resolution level, the feature map size is close to the original size of the input image, but its semantic information is relatively shallow, mainly encoding detailed features such as the edges, textures, and corners of sediment particles. At the top of the feature pyramid, the low-resolution level, the feature map size is significantly reduced, typically 1 / 32 of the input image size, but its semantic information is more profound, mainly encoding the overall shape, category, and spatial relationship of sediment particles with other sediment particles. The feature maps in the middle levels strike a balance between resolution and semantic abstraction, preserving some spatial location information while possessing some semantic discriminative ability.

[0045] Multi-scale feature encoders can employ CSPDarknet or similar backbone network structures, progressively reducing feature map resolution and increasing the number of channels through multiple stages of convolution and downsampling operations. After each stage, the network outputs the feature map for that stage, forming a feature pyramid. Unlike standard feature pyramid networks, multi-scale feature encoders embed scale-aware attention units after each layer of feature maps. These units use multiple sets of dilated convolutions with different dilation rates to extract features from different receptive fields in parallel. Then, they use learnable attention weights to weightedly fuse the feature maps from different receptive fields, enabling the network to dynamically adjust the receptive field size according to the actual scale distribution of sediment particles in the image.

[0046] Through a multi-scale feature pyramid, the model can simultaneously capture the overall outline of large sediment particles and the fine edges of small sediment particles, providing a rich feature base for subsequent sediment particle identification and separation. The scale-aware attention unit further enhances the model's adaptability to wide-gradation sediment particles.

[0047] The scale-aware feature modulator is a crucial bridge module connecting the upstream multi-scale reconstruction algorithm and the downstream recognition model. Its function is to adaptively modulate feature maps using compression coefficients at different image scales. This scale-aware feature modulator receives input from two sources. The first source is the feature pyramid output by the multi-scale feature encoder, from which the two feature maps with the strongest semantic representation are extracted as modulation targets. The feature maps with the strongest semantic representation typically refer to the two feature maps at the middle level of the feature pyramid, such as downsampled 1 / 16 and downsampled 1 / 32 feature maps. These two levels of feature maps achieve the best balance between the richness of semantic information and the fineness of spatial location. The second source is the image compression coefficient used in step 101, which is passed to the model as metadata along with the image slices.

[0048] The scale-aware feature modulator first maps the image compression coefficients to compression coefficient embedding vectors through a lightweight multilayer perceptron network. These embedding vectors express the resolution level of the current input image in a compact encoded form. Then, the scale-aware feature modulator performs linear feature modulation on two selected feature maps. The core formula for linear feature modulation is: the modulated feature map equals the original feature map multiplied by a scale factor plus a bias term. Both the scale factor and the bias term are generated from the compression coefficient embedding vectors using learned affine transformation parameters. Initially, the scale factor and bias term are initialized to zero; at this point, the modulated feature map equals the original feature map, equivalent to no modulation being applied. As the model learns during training, the scale factor and bias term are gradually adjusted, allowing the model to adaptively change the representation of the feature maps according to different values ​​of the compression coefficients. After modulation, the scale-aware feature modulator replaces the two modulated feature maps back in their original positions in the multi-scale feature pyramid, forming an updated multi-scale feature pyramid.

[0049] Through scale-aware feature modulation, the model can determine which compression level in the multi-scale reconstruction the current input image slice originates from. For example, when the input comes from a high-compression-ratio image, the model knows that the image is primarily used to identify large sediment particles, thus enhancing the filter response sensitive to large sediment particles at the feature level; when the input comes from a low-compression-ratio image, the model enhances the filter response sensitive to small sediment particles. This mechanism achieves end-to-end collaborative optimization between the upstream multi-scale reconstruction and the downstream recognition model.

[0050] The particle adhesion decoupling head is the core output module of the model. Its function is to simultaneously predict three different types of information based on a multi-scale feature pyramid, achieving end-to-end separation of adhered particles. This particle adhesion decoupling head receives the multi-scale feature pyramid updated by a scale-aware feature modulator as input and outputs three parallel prediction results: a binary segmentation mask, an adhesion probability map, and a center offset vector field. The binary segmentation mask is a single-channel image with the same size as the input image slice, where each pixel has a value of either zero or one. A pixel with a value of one indicates that it belongs to a sediment particle region, and a pixel with a value of zero indicates that it belongs to the background region. The binary segmentation mask solves the problem of where sediment particles are located, i.e., it determines whether each pixel in the image belongs to a sediment particle. The adhesion probability map is a single-channel image with the same size as the input image slice, where each pixel has a continuous probability value between zero and one. This probability value represents the probability that the pixel is in a particle adhesion region. A particle adhesion region refers to an area where two or more sediment particles are in contact and their boundaries are difficult to distinguish. Within the adhesion region, a pixel belongs to a sediment particle, but it's unclear which specific sediment particle instance it belongs to. The adhesion probability map resolves the question of whether sediment particles are adhered, providing crucial clues for subsequent instance separation. The center offset vector field is a two-channel image with the same size as the input image slice, where each pixel corresponds to a two-dimensional vector, i.e., dx and dy components. This vector represents the spatial offset from the current pixel to the center point of its corresponding particle. For a pixel located inside a sediment particle, this vector points to the geometric center of that particle; for a pixel located in the adhesion region, this vector points to the particle center to which it most likely belongs. The center offset vector field resolves the question of which sediment particle instance a pixel belongs to and is the core technical means for achieving adhesion separation. The three outputs have an inherent logical relationship. The binary segmentation mask first determines which pixels belong to sediment particles. Among these pixels belonging to sediment particles, the adhesion probability map marks which pixels are in the adhesion region. For pixels in the adhesion region, the center offset vector field provides the basis for assigning them to specific sediment particle instances. The three outputs work together to achieve the complete functionality from pixel-level segmentation to instance-level separation.

[0051] The instance assembler is the final module of the model. Its function is to convert the three raw outputs of the particle adhesion decoupling head into a structured list of sediment particle instances. The instance assembler takes the binary segmentation mask, adhesion probability map, and center offset vector field from the particle adhesion decoupling head as input, and outputs a list of all sediment particle instances identified in the current image slice. Each sediment particle instance contains the following information: the pixel-level mask coordinate set of the sediment particle, the bounding box position, the geometric center point coordinates, the identification confidence score, and a label indicating whether it comes from an adhesion separation region. The internal processing of the instance assembler is divided into four sub-steps.

[0052] The first sub-step is initial connected component segmentation. This step first performs connected component analysis on the binary segmentation mask, dividing interconnected pixel regions into an initial set of instance candidates. In the absence of adhesion, each connected component corresponds to an independent sand particle. In the presence of adhesion, multiple sand particles will merge into the same connected component.

[0053] The second sub-step is adhesion separation. This step targets regions in the adhesion probability map where the probability value exceeds a preset threshold, and uses a center offset vector field for refined separation. Specifically, for each pixel within the adhesion region, the particle center position predicted by its center offset vector is taken, and all pixels pointing to similar center positions are clustered into the same sediment particle instance. In this way, multiple sediment particles that were originally adhered together are separated into independent instances.

[0054] The third sub-step is boundary refinement. This step performs conditional random field (CRF) iterative optimization on the separated particle instance masks to improve the smoothness and edge accuracy of the masks. CRF optimization considers the spatial adjacency relationships between pixels and the consistency of pixel features, which can effectively eliminate holes and jagged edges in the mask, making the particle contours more consistent with the real physical morphology.

[0055] The fourth sub-step is confidence assessment and filtering. This step calculates a fusion confidence score for each particle instance based on multiple factors, including the instance's original confidence in the segmentation mask, the adhesion probability of its region, and whether the instance's size is within a reasonable range. Instances with a fusion confidence score below a preset lower limit are judged as low-quality recognition results and are filtered out. The remaining mud and sand instances constitute the final output.

[0056] A dataset of sampled sediment photos can be constructed using drone cameras to sample riverbeds in typical application scenarios, serving as the training dataset for the sediment particle recognition model. The collected photos must cover sediment particle sizes ranging from centimeters to meters, exhibit sufficient lithological diversity, and demonstrate diversity in watershed and river channel location. At least three photos should be included for each particle size, lithology, and different river channels. Based on the sampled sediment photo set, manual sediment contour mapping is performed using software such as QuPath or Labelme, generating a calibration dataset of approximately 200,000 calibrated sediment particles. The photo dataset and the manually calibrated dataset together constitute the training dataset for the sediment particle recognition model.

[0057] Figure 4 This is a schematic diagram showing the mud and sand particle identification results for each slice in an embodiment of the present invention. Figure 4 The outer boundary of each sediment particle is clearly marked.

[0058] In step 104, after mapping the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, the cross-scale occupancy area is determined. Based on the occupancy degree of sediment particle instances in the cross-scale occupancy area, the sediment particle instances in the cross-scale occupancy area are fused. The fused sediment particle instances in the cross-scale occupancy area and the sediment particle instances in the non-cross-scale occupancy area are combined to obtain the multi-scale fused sediment particle instance data. In one embodiment, after mapping the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, the cross-scale occupied area is determined, including: The sediment particle identification results of all image slices at each scale are stitched together to obtain the sediment particle identification results at each scale. Map the sediment particle identification results at each scale to the original image coordinate system of the UAV orthophoto; For the sediment particle identification results at any two scales in the original image coordinate system, the pixel occupancy overlap at the same pixel position is calculated based on the binary segmentation mask in the sediment particle identification results at the two scales. If the pixel occupancy overlap is greater than a preset overlap threshold, the pixel position is determined to be a cross-scale occupied pixel position. All cross-scale occupied pixel locations are formed into a cross-scale occupied region.

[0059] In the above embodiments, for each scale C j The sediment particle identification results of all image slices below are stitched together to obtain the C scale. j The sediment particle identification results below correspond to the binary segmentation mask M. j M j Each pixel value of 1 indicates that the pixel is occupied by a sediment particle instance identified at the current scale, and a value of 0 indicates that it is idle; then, the binary segmentation mask M is processed by bilinear interpolation. j Upsampled to the original image coordinate system of the UAV orthophoto, the upsampled occupancy mask M' is obtained. j It is used to align pixel positions at different scales.

[0060] For any two scales a and b (where a > b, i.e., a is a lower resolution scale and b is a higher resolution scale), the pixel overlap λ is defined as follows: λ(p) = M'_a(p) ∩ M_b(p) / M_b(p) Where p is the pixel position, M'_a(p) is the upsampling occupancy mask for large sediment particles in low-resolution images, and M_b(p) is the binary segmentation mask for small sediment particles in high-resolution images.

[0061] When λ(p) > τ (τ is a preset overlap threshold, ranging from 0.3 to 0.7), it is determined that there is cross-scale pixel occupancy at the pixel location. That is, the ghost image of large mud and sand particles in the low-resolution image substantially covers the physical space of small mud and sand particles in the original resolution, and all cross-scale occupied pixel locations form a cross-scale occupied region.

[0062] For cross-scale occupied areas, a differentiated fusion strategy is implemented: Suppose that the cross-scale occupied area is identified as a large sediment particle instance G in the low-resolution image and a small sediment particle instance S in the high-resolution image. Calculate the degree of occupancy Ω = avg(λ(p)) over p ∈ the occupied area; If Ω ≤ τ_low (low occupancy, e.g., ≤0.3): preserve S and mark it as recoverable detail; If τ_low < Ω < τ_high (occupied): retain both G and S, but remove S from the mask of G, that is, remove the pixel area occupied by S from the occupancy mask of G, and generate a correction mask M'_G = M_G - M_S. If Ω ≥ τ_high (high occupancy, e.g., ≥ 0.7): G is retained, S is marked as unrecoverable, but post-processing indicates that there may be particle size measurement errors in this region.

[0063] After removing the S pixel region, the mask of G has holes. Therefore, the convex hull filling algorithm is performed on the corrected mask M'_G of G to smoothly fill the depressions caused by the removal of small mud and sand particles. Connectivity analysis is performed on the filled M'_G to split the unconnected parts into independent mud and sand particle instances. The final output is the fused mud and sand particle instance set F = {S} ∪ {corrected G}.

[0064] In step 105, the particle size distribution of sediment is obtained based on the sample data of sediment particles.

[0065] In one embodiment, obtaining the sediment particle size distribution based on sediment particle instance data includes: Extract the binary segmentation mask and recognition scale label for each sediment particle instance in the sediment particle instance data; Principal component analysis is performed on each binary segmentation mask to determine the principal axis direction of the sediment particles, and the set of projection angles is determined based on the principal axis direction; the projection length of the sediment particles is calculated for each projection angle in the set of projection angles, and the median of the projection length is multiplied by the calibration coefficient to obtain the equivalent sieve particle size; Based on the equivalent sieve particle size and the identification scale label, the consistency index value and scale fit index value of particle size measurement are calculated. The scale fit index value is used to measure the degree of matching between the equivalent sieve particle size and the expected particle size range corresponding to the identification scale label. Based on the consistency index value and the scale adaptation index value, the particle size confidence level is obtained. Sediment particles with a particle size confidence level greater than the preset confidence level threshold are included in the sediment particle size distribution data of the river section.

[0066] In the above embodiments, obtaining the sediment particle size distribution at the river section scale from sediment particle instance data involves four core steps: First, extracting the binary segmentation mask and identification scale label from each sediment particle instance; then, calculating the equivalent sieving particle size based on the binary segmentation mask using an adaptive multi-directional projection algorithm; next, evaluating the confidence level of the particle size measurement results using the identification scale label; and finally, incorporating the high-confidence particle size data into the statistical distribution. The core innovation of this process lies in introducing prior information from upstream multi-scale identification into the particle size measurement stage, achieving closed-loop verification between identification and measurement.

[0067] The sediment particle instance data contains all identified sediment particle instances at the river reach scale. The data structure for each sediment particle instance includes a binary segmentation mask, an identification scale label, a bounding box, geometric center point coordinates, and an identification confidence score. The identification scale label indicates which compression ratio image the sediment particle was identified in, with label values ​​for large, medium, or small sediment particles, corresponding to expected particle size ranges in the meter, decimeter, and centimeter dimensions, respectively.

[0068] The core task of adaptive multi-directional projection particle size analysis is to convert the binary segmentation mask into an equivalent sieve particle size. Sieve particle size is a particle size metric used in traditional sediment analysis, defined as the side length of the smallest square sieve opening through which sediment particles can pass. In two-dimensional image analysis, the equivalent sieve particle size is usually approximated by a statistical measure of the projected lengths of sediment particles in different directions.

[0069] Determining the principal axis directions: For each binary segmentation mask, principal component analysis (PCA) is first performed. PCA is a statistical method used to find the direction with the largest variance in the data. Using the coordinates of all pixels in the binary segmentation mask as data points, PCA calculates two orthogonal principal axis directions. The first principal component direction corresponds to the longest extension direction of the sediment particles, i.e., the major axis direction of the sediment particles; the second principal component direction is perpendicular to the first principal component direction and corresponds to the minor axis direction of the sediment particles. These two directions together describe the orientation of the sediment particles in space.

[0070] Determination of the Adaptive Projection Angle Set: Unlike existing technologies that use random single projection or fixed three orthogonal direction projection, this invention adaptively determines the projection angle set based on principal component analysis results. Specifically, the projection angle set includes the following four directions: the first principal component direction (i.e., the principal axis direction), the direction perpendicular to the principal axis, and the directions forming angles of +45 degrees and -45 degrees with the principal axis direction. These four directions cover the main extension directions of sediment particles and their orthogonal directions, as well as two intermediate directions, which can comprehensively reflect the projection characteristics of sediment particles in different orientations. The reason for not using more directions is to strike a balance between measurement accuracy and computational efficiency; the empirical selection of four directions has been experimentally verified to achieve satisfactory results.

[0071] Calculation of projection length: For each projection angle in the set of projection angles, the projection length of the sediment particle at that angle needs to be calculated. The method for calculating the projection length is as follows: Project the coordinates of all pixels onto the unit vector of that projection angle to obtain a series of projection values. Subtract the minimum value from the maximum value; this is the projection length in that direction. Physically, this value is equivalent to the length of the shadow cast by the sediment particle in the direction perpendicular to the light rays when a pair of parallel light rays illuminate the sediment particle from that direction.

[0072] Determining the equivalent sieve particle size: After obtaining the projected lengths in four directions, the median of these projected lengths is calculated, and then multiplied by the calibration coefficient to obtain the equivalent sieve particle size. The median is used instead of the average value because the median is not sensitive to outliers. In actual measurements, small errors in mask extraction may cause the projected length in a certain direction to be abnormally large or small. Using the median can effectively resist the interference of such outliers. The calibration coefficient is an empirical parameter calculated by back-calculating from measurements of a standard sphere or a standard particle of known size. It is used to convert the pixel length in the image into the actual length in the physical world, and its value depends on the UAV's flight altitude, camera focal length, and image resolution.

[0073] Existing technologies typically output particle size measurement results directly without providing quantitative information on measurement uncertainty, and they do not utilize upstream identification results for cross-validation. This invention, however, calculates consistency index values ​​and scale fit index values ​​to assign a confidence score to each particle size measurement result, and uses this score to select reliable measurement results for inclusion in the final statistics.

[0074] Calculation of the consistency index: The consistency index measures the mutual consistency between measurement results from different projection directions. Specifically, it calculates the coefficient of variation (COP) of the four projection lengths, which is the standard deviation divided by the mean. A smaller COP indicates that the projection lengths in different directions are closer, suggesting that the sediment particles are close to spherical or equiaxed. In this case, the projection length is not sensitive to direction, and the reliability of particle size measurement is high. Conversely, a larger COP indicates that the sediment particles are highly anisotropic, with significant differences in projection lengths in different directions. In this case, the particle size measurement results are more sensitive to the choice of projection direction, and the reliability is relatively low. The consistency index is defined as 1 minus the COP, resulting in a value between 0 and 1. A larger value indicates better measurement consistency.

[0075] Calculation of the scale fit index: The scale fit index is a unique design feature of this scheme. Its core idea is to utilize the pre-defined correspondence between sediment particle size and compressibility coefficient, established in step 101, to cross-validate the particle size measurement results. Specifically, each sediment particle instance carries an identification scale label corresponding to an expected particle size range. For example, the expected particle size range corresponding to a large sediment particle label might be 1 to 10 meters, a medium sediment particle label to 0.1 to 1 meter, and a small sediment particle label to 0.01 to 0.1 meters. The scale fit index is used to measure the degree of matching between the measured equivalent sieve particle size and the expected particle size range corresponding to its identification scale label.

[0076] When calculating the scale fit index value, the first step is to determine whether the equivalent sieve particle size falls within the expected particle size range. If it does, a higher scale fit index value is assigned, indicating that the identification and measurement results corroborate each other. If the equivalent sieve particle size deviates significantly from the expected range—for example, an instance labeled with large sediment particles might have an equivalent sieve particle size at the centimeter level—it suggests a possible identification or measurement error, and a lower scale fit index value is assigned. The specific mathematical processing involves calculating the logarithmic deviation between the equivalent sieve particle size and the median of the expected particle size range, and then mapping it to a fraction between 0 and 1 using a decay function. The logarithmic deviation is used because particle size distributions typically follow a log-normal distribution, and deviation in logarithmic space better reflects the degree of deviation in practical terms.

[0077] The overall particle size confidence score is calculated by weighted summing of the consistency index and the scale fit index. The weights of these two indices can be adjusted based on the specific application scenario. In river sections with relatively regular particle shapes, the weight of the consistency index can be appropriately increased; in river sections with highly irregular particle shapes, the weight of the scale fit index can be appropriately increased. Generally, the weights of both indices are set to 0.5.

[0078] After obtaining the overall particle size confidence score for each sediment particle instance, a pre-set confidence threshold needs to be set to filter the measurement results. Only sediment particle instances with an overall particle size confidence score greater than this threshold are included in the final river section sediment particle size distribution statistics. Typical values ​​for the pre-set confidence threshold are between 0.7 and 0.9, with the specific value depending on the required data quality. A higher threshold is used when high-precision particle size distribution is needed for scientific analysis. When a rapid acquisition of overall trends is required and the data volume is sufficient, a lower threshold can be used, retaining more data but accepting a certain degree of measurement noise.

[0079] Particle instances with confidence levels below a threshold are not discarded directly. In a preferred embodiment, these low-confidence instances are individually labeled and output as auxiliary data for manual review by the user or for subsequent system optimization. For example, if a large number of low-confidence large sediment particle labels appear consecutively in a certain area, it may indicate that the particle size distribution in that area deviates from the preset magnitude classification, and the image compression coefficient in step 101 can be adaptively adjusted accordingly.

[0080] After the above screening, the remaining high-confidence sediment particle instances were included in the particle size distribution statistics. The statistical process first divided the equivalent sieve particle size into several particle size groups according to logarithmic intervals, such as less than 0.1 mm, 0.1 to 0.5 mm, 0.5 to 1 mm, etc., with the specific particle size division depending on the analysis requirements. Then, the area percentage of sediment particles in each particle size group was calculated, and a cumulative particle size distribution curve was plotted.

[0081] The final output of the river sediment particle size distribution data includes cumulative percentage curves for each particle size group, characteristic particle size values, and statistical parameters of the particle size distribution. Characteristic particle size values ​​include the median particle size, representing the 50% of the total mass of sediment particles smaller than this size, and commonly used quantile sizes. These data provide the foundational input for subsequent riverbed evolution analysis, sediment transport calculations, and aquatic ecosystem assessments.

[0082] In one embodiment, the method further includes: The contour of the binary segmentation mask for each sediment particle instance is extracted, and a continuously differentiable contour function is obtained by fitting a B-spline curve. The contour curvature of the continuously differentiable contour function is calculated, and local maxima of the contour curvature are identified as corner candidates. The best inscribed circle is fitted to each corner candidate to obtain the corner curvature radius. The roundness value is calculated based on the maximum value of the corner curvature radius. At the same time, a curvature distribution histogram is generated. Ellipse fitting is performed on the binary segmentation mask for each sediment particle instance to extract the eccentricity; Generate a shape parameter vector of sediment in the river section, the shape parameter vector including roundness value, eccentricity and curvature distribution histogram.

[0083] In the above embodiments, the extraction of shape parameters of sediment particles is a parallel processing step performed after the particle size distribution calculation. This process starts from the binary segmentation mask of each sediment particle instance and simultaneously extracts the particle shape features through two technical routes. The first route is based on contour analysis, using B-spline curve fitting and curvature calculation to obtain roundness values ​​and curvature distribution histograms. The second route is based on region analysis, using ellipse fitting to obtain eccentricity parameters. Finally, the roundness values, eccentricity, and curvature distribution histograms are analyzed. Figure 3 The parameters in each dimension are combined to form a shape parameter vector, which is used to characterize the morphological features of the particles.

[0084] For each instance of sediment particle, a binary segmentation mask is first required to extract its boundary contour. By tracing the boundary changes from 0 to 1 in the binary segmentation mask, a sequence of pixel coordinates arranged in clockwise or counterclockwise order can be extracted, which constitutes the original contour of the particle. The original contour consists of discrete pixels, with adjacent pixels connected at right angles or 45-degree angles, exhibiting a distinct jagged shape. This jaggedness is caused by the discrete sampling characteristics of the image.

[0085] The jagged shape of the original contour poses a serious problem for subsequent curvature calculations. Curvature, essentially a measure of the degree of curve bending, is highly sensitive to noise. Directly calculating curvature on a jagged contour composed of discrete pixels generates numerous spurious local maxima, making it impossible to distinguish between true particle corners and pixel-level random fluctuations. Therefore, it is necessary to smooth the original contour while preserving the basic shape characteristics of the particles, transforming it into a continuous and differentiable smooth curve. B-spline curves are a parametric curve representation method with excellent properties such as local support and higher-order continuity. Local support means that adjusting a control point only affects a small segment of the curve without causing global deformation, allowing B-spline curves to accurately fit various complex particle shapes. Higher-order continuity means that B-spline curves have continuous first and second derivatives, which are crucial for subsequent curvature calculations.

[0086] The fitting process includes: using the extracted original contour pixel coordinates as data points, and solving for the control point positions of the B-spline curve using the least squares method. The curve order is typically chosen to be cubic because, in cubic cases, the curve has continuous second derivatives, which satisfies the curvature calculation requirements while maintaining moderate computational complexity. The number of control points is adaptively determined based on the complexity of the particle contour; fewer control points are used for simple, nearly circular particles, while more control points are used for complex, irregular particles. The final result is a continuously differentiable contour function C(t) expressed in parametric form, where t is a parameter ranging from 0 to 1, and C(t) represents the two-dimensional coordinates of the corresponding point on the curve.

[0087] By fitting B-spline curves, discrete jagged pixels are transformed into smooth, continuous curves, effectively filtering out high-frequency noise while preserving the overall shape characteristics of the particles. This allows subsequent curvature calculations to accurately reflect the bending degree of the particle contour without being disturbed by pixel-level random fluctuations.

[0088] After obtaining the continuously differentiable profile function C(t), the curvature at each point on the curve can be calculated. The formula for curvature is: curvature equals the modulus of the cross product of the first and second derivatives divided by the cube of the modulus of the first derivative. The physical meaning of curvature is to describe the degree of bending of the curve at that point: the curvature at all points on a straight line is zero, the curvature of a circle is constant and inversely proportional to its radius, and the curvature at corners exhibits a large peak. A larger curvature value indicates a more pronounced bending at that point, while a smaller curvature value indicates that the point is closer to a straight line.

[0089] For a closed particle profile curve, traverse all parameter points and calculate the curvature value at each position to obtain the curvature function κ(t). This function records the distribution of the degree of curvature at each point along the profile.

[0090] Corner points are the locations where the curvature of sediment particles is most pronounced, corresponding to the sharp corners of particles that need to be identified in the traditional Wadell roundness formula. Corner locations can be automatically identified by analyzing the curvature function κ(t). Specifically, this involves finding local maxima of the curvature function, i.e., locations where the curvature value is greater than its left and right adjacent points. However, not all local maxima correspond to true corner points, as slight curvature fluctuations may exist even in smooth, curved regions. Therefore, a curvature threshold needs to be set, retaining only local maxima with curvature values ​​greater than this threshold as corner candidate points. The threshold can be adaptively determined by analyzing the statistical distribution of all curvature values, for example, by taking the mean curvature plus twice the standard deviation.

[0091] The identified corner candidates also need to be merged. In actual contours, the same physical corner may produce similar curvature peaks at multiple consecutive parameter positions. By setting a distance threshold, corner candidates with similar spatial positions are merged into a single corner, and the position with the largest curvature is taken as the final corner position.

[0092] By automatically identifying corner points through curvature analysis, the traditional Wadell roundness formula, which relies on manual corner point identification, is replaced, eliminating the subjectivity and non-repeatability of manual operation and achieving complete automation of roundness calculation.

[0093] For each identified corner point, its radius of curvature needs to be determined. The radius of curvature is the reciprocal of curvature and physically represents the degree of curvature in the vicinity of that point. A smaller radius of curvature indicates a sharper corner point; a larger radius of curvature indicates a more rounded corner point. However, the radius of curvature calculated directly from curvature can be affected by local noise. To obtain a more robust estimate of the corner radius of curvature, an inscribed circle fitting method is used: within a local neighborhood centered on the corner point, an arc segment on the curve is taken, and the optimal circle inscribed within this arc segment is found; the radius of this circle is the radius of curvature of the corner point. This method reduces the impact of single-point calculation errors by fitting the curve to multiple local points globally.

[0094] Wadell's roundness formula also requires knowing the maximum inscribed circle radius of the particle. The maximum inscribed circle is the largest circle that can be completely contained within the particle, and its radius reflects the overall size of the particle. The maximum inscribed circle radius can be quickly obtained through distance transformation. Distance transformation calculates the distance from each pixel in the mask to the nearest background pixel. After distance transformation, the value of the pixel inside the mud / sand particle represents the distance from that pixel to the boundary of the mud / sand particle. The maximum value of these distance values ​​is the maximum inscribed circle radius. The center of the maximum inscribed circle is located at the pixel position corresponding to this maximum value.

[0095] Wadell's roundness formula is defined as the sum of the radii of curvature of all corner points divided by the product of the number of corner points and the radius of the largest inscribed circle of the sediment particle. This ratio ranges from zero to one. When all corner points of the sediment particle are very sharp, the radii of curvature at each corner point are small, the numerator is small, and the roundness value is close to zero. When the sediment particle is nearly circular, there are no obvious corner points on the outline, and the number of corner points in the formula is very small or even close to zero. This situation requires special handling, and the roundness value is directly taken as a value close to one. When the number of corner points of the sediment particle is moderate and the radii of curvature at each corner point are close to the radius of the largest inscribed circle, the roundness value approaches one.

[0096] Roundness value is a comprehensive shape indicator, reflecting both the sharpness and number of corners. However, this comprehensiveness also leads to information loss: two sediment particles with the same roundness value may appear to have completely different shapes. For example, one sediment particle may have a deep indentation while another has three shallower indentations. Their roundness values ​​may be the same, but their appearances may differ significantly.

[0097] To overcome the information loss problem of traditional Wadell roundness values, a curvature distribution histogram is introduced as a supplementary descriptor for roundness values. Instead of compressing contour curvature information into a single value, the curvature distribution histogram preserves the distribution characteristics of curvature along the contour, thus providing a complete description of the overall angularity of the sediment particle surface.

[0098] The range of possible curvature values, from zero to the maximum curvature, is divided into several continuous intervals, each called a bin. The number of curvature values ​​of all pixels or all sampled points on the contour that fall into each bin is counted, resulting in a frequency histogram of the curvature distribution. To eliminate the influence of differences in sediment particle size, the histogram is usually normalized so that the sum of the frequencies of all bins equals 1.

[0099] Curvature distribution histograms provide rich shape information. The peak positions of the histogram reflect the most significant degree of curvature on the sediment particle profile. The dispersion of the histogram reflects the uniformity of the sediment particle corners. When sediment particles have multiple corners with varying degrees of sharpness, the histogram exhibits a multi-peak distribution. When sediment particles are nearly perfectly round, curvature values ​​concentrate in low-value regions. This information cannot be provided by a single roundness value.

[0100] Roundness values ​​and curvature distribution histograms complement each other. Roundness values ​​provide a concise numerical summary of the overall roundness of particles, facilitating rapid comparison and sorting. Curvature distribution histograms, on the other hand, retain detailed information, distinguishing sediment particles with the same roundness value but different shapes. The combination of the two ensures both simplicity of representation and avoids excessive information loss.

[0101] Ellipse fitting is another classic method in shape analysis, describing the shape of sediment particles from a global perspective. Unlike the local curvature methods in contour analysis, ellipse fitting focuses on the overall geometric characteristics of the particles. The goal of ellipse fitting is to find an ellipse that best approximates the region occupied by the sediment particle mask in a least-squares sense. Commonly used fitting methods include those based on eigenvalue decomposition of the covariance matrix and those based on algebraic distance minimization.

[0102] The method based on covariance matrix eigenvalue decomposition is computationally efficient. First, the mean of all pixel coordinates in the sediment particle mask is calculated to obtain the center of the ellipse. Then, the covariance matrix of the coordinates is calculated. The two eigenvectors of this matrix correspond to the major and minor axes of the ellipse, and the square roots of the two eigenvalues ​​correspond to the semi-lengths of the major and minor axes, respectively. Essentially, this method treats sediment particles as a two-dimensional set of points and uses their statistical properties to describe their shape.

[0103] The method based on minimizing algebraic distance offers better fitting accuracy. This method directly obtains the coefficients of the ellipse equation by solving a system of linear equations, minimizing the sum of the algebraic distances from all pixels to the elliptic curve. This approach can fit an ellipse that more closely resembles the actual boundaries of sediment particles, providing a more accurate description of irregular shapes.

[0104] From the ellipse fitting results, the lengths of the major and minor axes of the ellipse can be obtained. Eccentricity is defined as the square root of the quotient of the difference between the square of the major axis length and the square of the minor axis length, divided by the major axis length. The value of eccentricity ranges from zero to one. An eccentricity of zero indicates that the ellipse degenerates into a circle; the closer the eccentricity is to one, the more elongated the ellipse. Eccentricity describes the overall elongation of the particle and is another important dimension of particle shape.

[0105] Besides eccentricity, ellipse fitting can also output the orientation angle of the ellipse, indicating the direction of the major axis of the sediment particles. This orientation angle information can be used to analyze the directional alignment characteristics of particles on the riverbed. For example, under unidirectional water transport and deposition, non-equiaxed particles may exhibit a certain dominant orientation. Furthermore, by comparing the difference between the ellipse and the actual sediment particle mask, a measure of particle irregularity can be obtained; a larger difference indicates a more severe deviation of the sediment particles from the elliptical shape.

[0106] For each sediment particle instance, its roundness value, eccentricity, and curvature distribution histogram are combined into a shape parameter vector. The roundness value is a scalar, the eccentricity is also a scalar, and the curvature distribution histogram is a vector. Therefore, the shape parameter vector is actually a mixture of scalars and vectors, and in actual storage, the curvature distribution histogram is embedded as a vector parameter.

[0107] By summing the shape parameter vectors of all sediment particle instances, we can obtain the shape statistical characteristics at the river section scale. Specifically, this includes: the statistical distribution of roundness values, used to describe the overall roundness of sediment particles in the river section; the statistical distribution of eccentricity, used to describe the elongation of sediment particles; and the average curvature distribution histogram, which is obtained by weighting the curvature distribution histograms of all sediment particles according to the number of particles, to obtain the typical curvature distribution pattern at the river section scale.

[0108] In practical applications, shape parameters are often analyzed in conjunction with particle size distribution. For example, the changing trends of sphericity of sediment particles in different particle size groups can be analyzed. Larger sediment particles may exhibit lower sphericity due to their greater tendency to break, while smaller sediment particles may exhibit higher sphericity due to their preferential rounding. This correlation analysis between particle size and shape provides richer quantitative information for riverbed evolution studies.

[0109] This invention also proposes a low-altitude measurement device for sediment particle size at the river section scale, the principle of which is similar to the low-altitude measurement method for sediment particle size at the river section scale, and will not be described in detail here.

[0110] Figure 5 This is a schematic diagram of the structure of the low-altitude measurement device for sediment particle size at the river section scale in an embodiment of the present invention, including: The multi-scale compression module 501 is used to perform multi-scale compression on the UAV orthophoto at the river section scale by pre-setting multiple different image compression coefficients to obtain images at multiple scales. The slicing module 502 is used to perform recursive slicing of the image at each scale based on the estimated video memory usage, so as to obtain multiple image slices at each scale. The recognition module 503 is used to input each image slice and the corresponding image compression coefficient into the sediment particle recognition model to obtain the sediment particle recognition result of each image slice. The sediment particle recognition model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. The fusion module 504 is used to map the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, determine the cross-scale occupied area, and based on the occupancy degree of sediment particle instances in the cross-scale occupied area, fuse the sediment particle instances in the cross-scale occupied area, and combine the fused sediment particle instances in the cross-scale occupied area and the sediment particle instances in the non-cross-scale occupied area to obtain multi-scale fused sediment particle instance data. The particle size measurement module 505 is used to obtain the particle size distribution of sediment based on sample data of sediment particles.

[0111] In one embodiment, the slicing module is used for: For each scale of the image, image slices are divided according to the reference slice size, and the overlapping area between adjacent image slices is maintained by a preset overlap rate; For image slices whose boundaries are smaller than the reference slice size, mirror filling is used to expand them to the reference slice size, generating a slice queue containing all image slices; For each image slice in the slice queue, the video memory usage is calculated based on the size and content complexity of the image slice. If the video memory usage is greater than the video memory usage threshold, the image slice is recursively segmented using a new baseline slice size until the video memory usage of each image slice after segmentation is less than or equal to the video memory usage threshold, or the size of each image slice after segmentation reaches the lower bound of the size.

[0112] In one embodiment, the sediment particle identification model includes: A multi-scale feature encoder is used to generate a multi-scale feature pyramid from input image slices. The multi-scale feature pyramid includes multiple feature maps with different resolutions and semantics. The scale-aware feature modulator is used to linearly modulate the two feature maps with the most semantic representation ability in the multi-scale feature pyramid based on the image compression coefficients corresponding to the input image slices, and then replaces the two feature maps with the most semantic representation ability in the multi-scale feature pyramid with the modulated two feature maps. The particle adhesion decoupling head is used to predict the pixel-level segmentation mask, the adhesion probability between particles, and the offset vector of each pixel pointing to the center of its respective particle from the current multi-scale feature pyramid, and obtain the binary segmentation mask, adhesion probability map and center offset vector field respectively. An instance assembler is used to obtain the mud and sand particle identification results of the input image slice based on the binary segmentation mask, the adhesion probability map and the center offset vector field. The mud and sand particle identification results include the binary segmentation mask and the identification scale label for each mud and sand particle instance.

[0113] In one embodiment, the fusion module is used for: The sediment particle identification results of all image slices at each scale are stitched together to obtain the sediment particle identification results at each scale. Map the sediment particle identification results at each scale to the original image coordinate system of the UAV orthophoto; For the sediment particle identification results at any two scales in the original image coordinate system, the pixel occupancy overlap at the same pixel position is calculated based on the binary segmentation mask in the sediment particle identification results at the two scales. If the pixel occupancy overlap is greater than a preset overlap threshold, the pixel position is determined to be a cross-scale occupied pixel position. All cross-scale occupied pixel locations are formed into a cross-scale occupied region.

[0114] In one embodiment, the particle size measurement module is used for: Extract the binary segmentation mask and recognition scale label for each sediment particle instance in the sediment particle instance data; Principal component analysis is performed on each binary segmentation mask to determine the principal axis direction of the sediment particles, and the set of projection angles is determined based on the principal axis direction; the projection length of the sediment particles is calculated for each projection angle in the set of projection angles, and the median of the projection length is multiplied by the calibration coefficient to obtain the equivalent sieve particle size; Based on the equivalent sieve particle size and the identification scale label, the consistency index value and scale fit index value of particle size measurement are calculated. The scale fit index value is used to measure the degree of matching between the equivalent sieve particle size and the expected particle size range corresponding to the identification scale label. Based on the consistency index value and the scale adaptation index value, the particle size confidence level is obtained. Sediment particles with a particle size confidence level greater than the preset confidence level threshold are included in the sediment particle size distribution data of the river section.

[0115] In one embodiment, the particle size measurement module is used for: The contour of the binary segmentation mask for each sediment particle instance is extracted, and a continuously differentiable contour function is obtained by fitting a B-spline curve. The contour curvature of the continuously differentiable contour function is calculated, and local maxima of the contour curvature are identified as corner candidates. The best inscribed circle is fitted to each corner candidate to obtain the corner curvature radius. The roundness value is calculated based on the maximum value of the corner curvature radius. At the same time, a curvature distribution histogram is generated. Ellipse fitting is performed on the binary segmentation mask for each sediment particle instance to extract the eccentricity; Generate a shape parameter vector of sediment in the river section, the shape parameter vector including roundness value, eccentricity and curvature distribution histogram.

[0116] This invention also provides a computer device. Figure 6 This is a schematic diagram of a computer device in an embodiment of the present invention. The computer device 600 includes a memory 610, a processor 620, and a computer program 630 stored in the memory 610 and executable on the processor 620. When the processor 620 executes the computer program 630, it implements a method.

[0117] This invention also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for low-altitude measurement of sediment particle size at the river section scale.

[0118] This invention also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-mentioned method for low-altitude measurement of sediment particle size at the river section scale.

[0119] In this embodiment of the invention, multiple different image compression coefficients are preset to perform multi-scale compression on UAV orthophotos at the river section scale, resulting in images of multiple scales. This allows the same image to exhibit different particle size scales under different compression coefficients, providing a multi-resolution information basis for subsequent identification. The amount of low-scale image data after compression is significantly reduced, avoiding the computational resource pressure caused by directly processing ultra-high-resolution orthophotos. The memory usage of image slices is calculated, and automatic recursive segmentation is performed when the memory usage exceeds the memory limit, ensuring that the subsequent sediment particle identification model runs stably under limited memory, without the need for manually preset slice sizes. Within the allowable memory range, the slice size is retained as large as possible to reduce the number of slices, thereby reducing redundant calculations caused by overlapping slices and the complexity of subsequent fusion. The image compression coefficient is used as explicit conditional information input to the sediment particle identification model, allowing the model to know which compression scale the currently processed image slice comes from, thus adopting an appropriate identification strategy at different scales and improving the accuracy and consistency of cross-scale identification. In high-compression (low-resolution) images, sediment particle identification models focus on large-scale structural features; in low-compression (high-resolution) images, they retain sensitivity to small sediment particles. Combining these two approaches allows the sediment particle identification model to simultaneously cover a wide particle size range. The same particle may be identified in images at different scales, and direct stitching would lead to duplicate counting. By using cross-scale occupancy region detection and fusion based on occupancy degree, it is possible to accurately determine which sediment particle instances represent the same physical particle, avoiding duplication or omission. The fusion strategy based on occupancy degree allows the scale results with higher confidence and clearer boundaries to dominate the fusion process, thereby improving the quality of the final particle instance data. The fused sediment particle instance data integrates the advantages of each scale, including the overall morphology of large sediment particles while preserving the fine boundaries of small sediment particles, forming complete information on particle distribution at the river section scale.

[0120] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0121] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0122] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0123] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0124] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above descriptions are merely specific embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for low-altitude measurement of sediment particle size at the river section scale, characterized in that, include: By presetting multiple different image compression coefficients, multi-scale compression is performed on the orthophotos of the UAV at the river section scale to obtain images at multiple scales. Recursively slice the image at each scale based on the estimated video memory usage to obtain multiple image slices at each scale. Each image slice and its corresponding image compression coefficient are input into the sediment particle recognition model to obtain the sediment particle recognition result for each image slice. The sediment particle recognition model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. After mapping the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, the cross-scale occupancy area is determined. Based on the occupancy degree of sediment particle instances in the cross-scale occupancy area, the sediment particle instances in the cross-scale occupancy area are fused. Combining the fused sediment particle instances in the cross-scale occupancy area and the sediment particle instances in the non-cross-scale occupancy area, the multi-scale fused sediment particle instance data is obtained. Based on the sample data of sediment particles, the particle size distribution of sediment was obtained.

2. The method as described in claim 1, characterized in that, Recursively slice the image at each scale based on memory usage estimation, resulting in multiple image slices at each scale, including: For each scale of the image, image slices are divided according to the reference slice size, and the overlapping area between adjacent image slices is maintained with a preset overlap rate; For image slices whose boundaries are smaller than the reference slice size, mirror filling is used to expand them to the reference slice size, generating a slice queue containing all image slices; For each image slice in the slice queue, the video memory usage is calculated based on the size and content complexity of the image slice. If the video memory usage is greater than the video memory usage threshold, the image slice is recursively segmented using a new baseline slice size until the video memory usage of each image slice after segmentation is less than or equal to the video memory usage threshold, or the size of each image slice after segmentation reaches the lower bound of the size.

3. The method as described in claim 1, characterized in that, The sediment particle identification model includes: A multi-scale feature encoder is used to generate a multi-scale feature pyramid from input image slices. The multi-scale feature pyramid includes multiple feature maps with different resolutions and semantics. The scale-aware feature modulator is used to linearly modulate the two feature maps with the most semantic representation ability in the multi-scale feature pyramid based on the image compression coefficients corresponding to the input image slices, and then replaces the two feature maps with the most semantic representation ability in the multi-scale feature pyramid with the modulated two feature maps. The particle adhesion decoupling head is used to predict the pixel-level segmentation mask, the adhesion probability between particles, and the offset vector of each pixel pointing to the center of its respective particle from the current multi-scale feature pyramid, and obtain the binary segmentation mask, adhesion probability map and center offset vector field respectively. An instance assembler is used to obtain the mud and sand particle identification results of the input image slice based on the binary segmentation mask, the adhesion probability map and the center offset vector field. The mud and sand particle identification results include the binary segmentation mask and the identification scale label for each mud and sand particle instance.

4. The method as described in claim 1, characterized in that, After mapping the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, the cross-scale occupied area is determined, including: The sediment particle identification results of all image slices at each scale are stitched together to obtain the sediment particle identification results at each scale. Map the sediment particle identification results at each scale to the original image coordinate system of the UAV orthophoto; For the sediment particle identification results at any two scales in the original image coordinate system, the pixel occupancy overlap at the same pixel position is calculated based on the binary segmentation mask in the sediment particle identification results at the two scales. If the pixel occupancy overlap is greater than a preset overlap threshold, the pixel position is determined to be a cross-scale occupied pixel position. All cross-scale occupied pixel locations are formed into a cross-scale occupied region.

5. The method as described in claim 1, characterized in that, Based on the sample data of sediment particles, the sediment particle size distribution was obtained, including: Extract the binary segmentation mask and identification scale label for each sediment particle instance in the sediment particle instance data; Principal component analysis is performed on each binary segmentation mask to determine the principal axis direction of the sediment particles, and the set of projection angles is determined based on the principal axis direction; the projection length of the sediment particles is calculated for each projection angle in the set of projection angles, and the median of the projection length is multiplied by the calibration coefficient to obtain the equivalent sieve particle size; Based on the equivalent sieve particle size and the identification scale label, the consistency index value and scale fit index value of particle size measurement are calculated. The scale fit index value is used to measure the degree of matching between the equivalent sieve particle size and the expected particle size range corresponding to the identification scale label. Based on the consistency index value and the scale adaptation index value, the particle size confidence level is obtained. Sediment particles with a particle size confidence level greater than the preset confidence level threshold are included in the sediment particle size distribution data of the river section.

6. The method as described in claim 5, characterized in that, Also includes: The contour of the binary segmentation mask for each sediment particle instance is extracted, and a continuously differentiable contour function is obtained by fitting a B-spline curve. Calculate the profile curvature of a continuously differentiable profile function and identify local maxima of profile curvature as corner candidates; fit the best inscribed circle to each corner candidate to obtain the corner curvature radius; calculate the roundness value based on the maximum corner curvature radius; and generate a curvature distribution histogram. Ellipse fitting is performed on the binary segmentation mask for each sediment particle instance to extract the eccentricity; Generate a shape parameter vector of sediment in the river section, the shape parameter vector including roundness value, eccentricity and curvature distribution histogram.

7. A low-altitude measurement device for sediment particle size at the river section scale, characterized in that, include: The multi-scale compression module is used to perform multi-scale compression on UAV orthophotos at the river section scale by presetting multiple different image compression coefficients to obtain images at multiple scales. The slicing module is used to recursively slice the image at each scale based on the estimated video memory usage, resulting in multiple image slices at each scale. The identification module is used to input each image slice and its corresponding image compression coefficient into the sediment particle identification model to obtain the sediment particle identification result for each image slice. The sediment particle identification model is obtained by training a deep learning-based instance segmentation model using historical UAV orthophotos at the river section scale. The fusion module is used to map the sediment particle identification results of all image slices to the original image coordinate system of the UAV orthophoto, determine the cross-scale occupied area, and based on the occupancy degree of sediment particle instances in the cross-scale occupied area, fuse the sediment particle instances in the cross-scale occupied area, and combine the fused sediment particle instances in the cross-scale occupied area and the sediment particle instances in the non-cross-scale occupied area to obtain multi-scale fused sediment particle instance data. The particle size measurement module is used to obtain the particle size distribution of sediment based on sample data of sediment particles.

8. 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 computer program, it implements the method of any one of claims 1 to 6.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 6.

10. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the method of any one of claims 1 to 6.

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