Construction method of bilinear residual filter applied to pulverized coal particle measurement

Abstract

The invention relates to the technical field of image enhancement recognition, in particular to a construction method of a bilinear residual filter applied to pulverized coal particle measurement, which comprises the following steps: inserting a scaling operator B to design a bilinear residual unit in the bilinear residual filter based on the basic principle of bilinear interpolation; constructing through Taylor expansion from a mathematical angle and optimizing a filter by combining with an optimization objective function; designing a sampling operator to enable a scaling operator to meet the requirement of a low-frequency span in a sampling process; and a final optimized bilinear residual filter is obtained by considering the reciprocal relationship between the scaling multiples. The filter designed by the invention not only can accurately recover edge details in an image scaling process, but also can keep stable segmentation performance in a complex environment, and provides a better solution for applications such as image processing, target detection and coal particle size measurement.

Description

Technical Field

[0001] The present application relates to the technical field of image enhancement and recognition, and in particular to a method for constructing a bilinear residual filter used in coal powder particle measurement. Background Art

[0002] In recent years, the country has continuously increased its attention to coal mine safety, and the safety situation has improved. However, accidents still occur, indicating that safety challenges remain. The release of gas and coal particles is a common phenomenon during mining, transportation, and crushing operations in coal mines, and the amount released varies depending on the operation. Gas explosions are primarily caused by the widespread distribution of methane gas within coal mines, and the size characteristics of coal particles play a crucial role in this process. Coal particle size directly affects the diffusion, accumulation, and propagation paths of methane, and also influences its behavior during adsorption, diffusion, and emission. These differences in properties provide a theoretical basis for in-depth research and prediction of methane behavior in coal mines. Notably, coal particles smaller than 75 microns pose a serious safety threat due to their extremely high explosion susceptibility. Therefore, using high-precision detection methods to analyze coal particle size distribution has important academic and practical significance for evaluating the effectiveness of coal mine dust control facilities and improving workplace safety.

[0003] With the development of image processing technology and the application of deep learning techniques in image processing, image analysis has made significant progress in the field of particle detection and segmentation. However, while deep learning methods have demonstrated end-to-end efficiency and accuracy in coal particle segmentation, they still face challenges. In coal mining environments, image recognition accuracy is poor, and the recognition quality of target edge features is low, making it unable to effectively address the complexity and fine-grained measurement requirements of coal dust particles. Summary of the Invention

[0004] The technical problem to be solved by the present invention is that the existing image processing algorithms have low recognition quality for target edge features, and thus cannot effectively cope with the complexity and fine-grained measurement requirements of coal dust particles.

[0005] To this end, the present invention provides a method for constructing a bilinear residual filter applied in coal powder particle measurement, which efficiently performs image upsampling and downsampling, effectively restores the edge features and high-frequency detail information of the image, and improves the overall quality of the image.

[0006] The technical solution adopted by the present invention to solve its technical problem is:

[0007] A method for constructing a bilinear residual filter for use in coal powder particle measurement comprises the following steps:

[0008] Step 1: Based on the basic principle of bilinear interpolation, a scaling operator B is inserted to design a bilinear residual unit in the bilinear residual filter;

[0009] Step 2: From a mathematical perspective, the filter is optimized by Taylor expansion and combined with the optimization objective function;

[0010] Step 3: Design the sampling operator so that the scaling operator can meet the low-frequency span requirement during the sampling process;

[0011] Step 4: Consider the inverse relationship between the scaling factors to obtain the final optimized bilinear residual filter.

[0012] Furthermore, in step 1, the bilinear residual filter has a bilinear residual unit, and the bilinear residual unit includes an upsampler, a downsampler and a subtractor, wherein the scaling operator B is used as a structural component of the bilinear residual unit for upsampling and downsampling of the image.

[0013] Furthermore, the scaling operator B satisfies the characteristic of uniform scaling in space, defining a linear mapping function where x′∈G i ,i∈1,2,…, α is the scale factor, then B should satisfy:

[0014] Furthermore, in step 2, a Gaussian function is used To simulate the singularity features, and consider all possible offsets and scale changes by stretching the sub-pixel offset μ and the standard deviation σ; by minimizing the distance between the downsampled Gaussian function f and the ideal or expected Gaussian function f, the singularity features are accurately preserved.

[0015] Furthermore, in step 2, the objective function is designed Where M is the normalization factor, which is equal to the number of summation terms; μ is the mean; and σ is the standard deviation.

[0016] Furthermore, in step 2, based on the linear characteristics of the filter, the residual layer E(x) used to represent the edge contour is expressed as E(x)=a×I(x)+b, where a and b are known constants. Taylor expansion at any point x0 can be obtained: in, Available

[0017] Furthermore, in step 3, a new objective function is defined for the low-frequency span: Where B is the discrete differential operator, b j is the input signal.

[0018] Furthermore, in step 4, the objective function after optimization constraint is obtained by combining the objective functions in steps 2 and 3. Among them, η and ε are two learnable parameters used to determine the priority of the two objective functions, M is the normalization factor, and N is the number of samples.

[0019] Furthermore, in the step 4, a basic scaling factor α is defined to represent the scaling ratio of a certain dimension of the image (such as width or height). When downsampling is performed using this factor, the size of the image is reduced to 1 / α of the original size. The downsampled image is upsampled using the reciprocal factor 1 / α to achieve the effect of restoring the image to a size close to the original size.

[0020] Furthermore, in step 4, the Lagrange multiplier rule is applied based on the objective function after optimization constraint, combined with the reciprocal relationship of the scaling multiple, to obtain the final optimized bilinear residual filter

[0021] The beneficial effects of the present invention are as follows: based on the basic principles of bilinear interpolation, this application optimizes the design of the bilinear residual unit within the bilinear residual filter to ensure that key detail information is effectively retained during image scaling and reduce the loss of high-frequency information caused by interpolation. Furthermore, by combining residual information extraction and compensation mechanisms, the filter's ability to preserve edge features is enhanced, thereby improving image quality and segmentation accuracy after scaling. Furthermore, an objective function is further constructed and optimized to enable the scaling operator to accurately preserve singularity features in the image. Through reasonable mathematical modeling and constraints, the filter is ensured to accurately capture edge features at different scales, avoiding edge blurring or information loss during image scaling. Subsequently, a suitable sampling operator is designed to ensure that the scaling operator's sampling process meets low-frequency span requirements. During this process, bandwidth constraints and frequency domain characteristics are fully considered, enabling the filter to effectively suppress aliasing effects during both upsampling and downsampling, thereby improving image reconstruction quality and visual consistency. Finally, by comprehensively considering the inverse relationship between scaling factors and combining the aforementioned optimization designs, a bilinear residual filter is ultimately derived that meets the characteristics of linear invariance, low-frequency span control, and singularity preservation. This filter can not only accurately restore edge details during image scaling, but also maintain stable segmentation performance in complex environments, providing a better solution for applications such as image processing, target detection, and coal particle size measurement. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The present invention will be further described below with reference to the accompanying drawings and examples.

[0023] Figure 1 It is a flow chart of a method for constructing a bilinear residual filter used in coal powder particle measurement in the present invention.

[0024] Figure 2 It is a block diagram of the method for constructing a bilinear residual filter in the present invention.

[0025] Figure 3 Schematic diagram of the bilinear interpolation algorithm in the present invention.

[0026] Figure 4 Schematic diagram of a basic unit of the bilinear residual filter in the present invention.

[0027] Figure 5 This is a comparison chart of the results of using the bilinear residual filter in this application for image enhancement processing and other image enhancement algorithms to identify the coal sample combination A.

[0028] Figure 6 This is a comparison chart of the results of using the bilinear residual filter in this application for image enhancement processing and other image enhancement algorithms to identify coal sample combination B.

[0029] Figure 7 This is a comparison chart of the results of identifying coal sample combination C using the bilinear residual filter in this application for image enhancement processing and other image enhancement algorithms.

[0030] Figure 8 It is a schematic diagram of the results of coal particle size measurement using image enhancement and identification using the bilinear residual filter in this application. DETAILED DESCRIPTION

[0031] The present invention will now be described in further detail with reference to the accompanying drawings, which are simplified schematic diagrams that illustrate the basic structure of the present invention in a schematic manner.

[0032] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings. They are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, features defined as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0033] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they may refer to fixed, detachable, or integral connections; mechanical or electrical connections; direct or indirect connections through an intermediate medium; and internal communication between two components. Those skilled in the art will understand the specific meanings of the above terms in the present invention based on the specific circumstances.

[0034] A method for constructing a bilinear residual filter for use in coal powder particle measurement includes:

[0035] Bilinear interpolation is a common image processing algorithm that is widely used to solve the problem of estimating unknown pixel values ​​between two-dimensional data points. The core idea is to perform two linear interpolations in the horizontal and vertical directions respectively to generate a smoother and more natural transition effect. Specifically, when the coordinates of the target pixel are between four known pixel points (forming a 2×2 pixel block), the two adjacent pixel points are first linearly interpolated in the horizontal direction to obtain two intermediate values; then, the two intermediate values ​​are linearly interpolated again in the vertical direction to infer the final value of the target pixel. We can use Figure 3 To illustrate, the core idea of ​​bilinear interpolation is to perform linear interpolation in both x and y directions. Assume Q 11 , Q 12 , Q 21 , Q 22 Q is the position of the four pixels required for scaling. 11 =(x1,y1),Q 12 =(x1,y2),Q 21 =(x2,y1),Q 22 =(x2,y2), where f(*) is the pixel value at position *.

[0036] The final bilinear interpolation calculation result is:

[0037]

[0038] The bilinear residual unit is the basic structure of the bilinear residual filter. Figure 4 As shown, it consists of three parts: bilinear upsampler, bilinear downsampler and subtractor. Figure 4 In the figure, blue, yellow and green rectangular blocks are used to represent the edge contour of the image. According to the characteristics of signal transmission, the residual layer can be obtained to represent the edge contour of the image E(x)=I(x)-B(B(I(x))), where I(x) is the original image and B is the bilinear interpolation scaling operator.

[0039] However, according to the basic theory of bilinear interpolation, the bilinear interpolation operation can be expressed as f(x,y)=f(Q 11 )*ω 11 +f(Q 21 )*ω 21 +f(Q 12 )*ω 12 +f(Q 22 )*ω 22 =KX+b, where ω 11 ,ω 12 ,ω 21 ,ω 22 are the weights of the four points determined, and the matrix they form is recorded as K. K, X, and b are the corresponding matrices, where X is the matrix composed of the four f(*) values, and b is the bias matrix to prevent it from being 0. f(x, y) = Q 11 *ω 11 +Q 21 *ω 21 +Q 12 *ω 12 +Q 22 *ω 22 =KX+b is recorded as B and is brought into E(x)=I(x)-B(B(I(x))) to get E=IK′(KI+b)+b′=(IK′ T K)IK′ T b+b′, analysis shows that it satisfies the linear property.

[0040] Because the bilinear residual unit satisfies the linear property, the scaling operator B is used for up and down sampling of the image as the structural component of the bilinear residual unit, so the scaling operator B should also satisfy the characteristics of uniform scaling in space, that is, for low-resolution images or feature maps P l+1 Linearly map to high-resolution image I through linear function l Above, or high resolution image I l Pixels or low-resolution images or feature maps P on l+1 Based on this, we define the linear mapping function where x′∈G i ,i∈1,2,…, α is the scale factor, its value is not fixed, then B should satisfy the following expression:

[0041]

[0042] Among them, x' is the pixel position of the scaled image, and x is the pixel position of the original image obtained through linear mapping. Then the x obtained by the above formula is o is the pixel value obtained by the B operator at the position of the pixel point x′ mapped in the original image.

[0043] Step 2: Construct and optimize the objective function so that the scaling operator in the filter can accurately preserve the singularity features in the image.

[0044] In the image sampling process, it is inevitable to lose some high-frequency information and singular points in the image (such as edges and corners). This high-frequency information is crucial for the image's detail representation and feature recognition, and its loss often leads to image quality degradation and blurred feature information. Therefore, when designing the sampling operator, it is necessary to fully consider how to retain this key information to the maximum extent possible, especially to ensure that the shape of the singular points remains consistent. To this end, the Gaussian function is used. To simulate the singularity features, and consider all possible offsets and scale changes by sub-pixel offset μ and stretching the standard deviation σ. Ultimately, by minimizing the distance between the downsampled Gaussian function f and the ideal or expected f, the singularity features are accurately preserved. This optimization process constructs an objective function to ensure the effective preservation of important information during the scale transformation, so that even after multiple upsampling or downsampling, the edge features and key structures of the image can still be accurately reproduced. The specific objective function is as follows:

[0045]

[0046] Where M is the normalization factor, which is equal to the number of summation terms; μ is the mean; and σ is the standard deviation.

[0047] From the previous step, we can see that the designed filter is linear, so Figure 4 In the equation, E(x) and I(x) are linearly related, so E(x) = a × I(x) + b, where a and b are known constants. Taylor expansion of this equation at any point x0 yields: Among them, x-x0 is very small, so we can get Here, α, β, and γ are adjustable linear coefficients. This formula shows that the residual information obtained is exponentially related to the first-order and second-order differences of the input signal. First-order differences are primarily used to extract coarse edge information in an image, outlining the overall contours and basic shape features of the target. They provide clear visual guidance in complex scenes and are crucial for identifying image structure. In contrast, second-order differences focus more on extracting fine edges, accurately locating corners and small details, enabling more refined edge detection. This precise edge information extraction is particularly critical in image segmentation tasks, revealing subtle changes in the image and ensuring the complete capture of complex shapes and textures. In summary, the designed bilinear residual filter not only exhibits excellent edge-preserving performance, effectively preserving important edge features during scaling or resampling, but also exhibits strong adaptability. By combining first- and second-order differences, the filter optimizes image processing at different levels, resulting in more accurate edge detection and providing strong support for high-quality image segmentation and feature extraction.

[0048] During the scale transformation process, the optimization objective function we constructed follows the singularity preservation principle, ensuring that key features such as edges and corners are not lost or deformed due to scaling. Mathematically, we derive the multiples between the residual information and the first-order and second-order differences through Taylor expansion to ensure the correct mapping relationship between singularities at different scales. As a result, the filter maintains the overall edge contour, achieving the effect of edge preservation.

[0049] Step three, design the sampling operator to ensure that the scaling operator sampling process meets the requirements of the low-frequency span.

[0050] The camera's built-in point spread function (PSF) and anti-aliasing filters play a crucial role in image processing. These filters constrain the bandwidth of the input signal (i.e., the scene) based on the sensor's sampling rate to ensure that the signal satisfies or nearly satisfies the Nyquist sampling theorem, thus influencing the upsampling and downsampling processes. During upsampling, although the filter limits the bandwidth of the original signal, resulting in an improvement in resolution after upsampling, the actual increase in detail is limited by the original signal's bandwidth. As a result, while the image may appear sharper, its inherent information richness remains unchanged. In contrast, during downsampling, the filter plays an even more crucial role, effectively removing high-frequency components that exceed the sensor's sampling rate, preventing artifacts caused by aliasing and ensuring that the downsampled image remains clear. Therefore, when designing a sampling operator, it is crucial to ensure that the sampling process appropriately preserves low-frequency signals to optimize image quality. "Low-frequency span" here refers to the proportion or range of low-frequency components in the image signal, a key factor affecting image quality. Precisely controlling the low-frequency span helps optimize sampling efficiency, enabling images to maintain high clarity and rich details under different operating conditions.

[0051] To this end, we define a new objective function for low-frequency span:

[0052]

[0053] Where B is the discrete differential operator, b j is the input signal sample, N is the number of samples, so the above L2 is equivalent to minimizing the power spectrum in the frequency domain High-frequency components represent rapid changes in the signal (such as noise or fine details), while low-frequency components represent the overall structure or smooth parts of the signal. When the discrete differential operator B is applied to the signal in the spatial (or time) domain, it is equivalent to applying a high-pass filter in the frequency domain. Therefore, it effectively controls the eigenvalue distribution of the Laplacian matrix, suppressing high-frequency components while enhancing the expressiveness of low-frequency components, making the signal smoother and more reconstructible.

[0054] In step 4, the inverse relationship between the scaling factors is comprehensively considered, and combined with the aforementioned optimization designs, a bilinear residual filter that satisfies the linear invariance, low-frequency span control, and singularity preservation characteristics is finally obtained.

[0055] Combining the objective functions proposed in the first two steps, we can obtain the following objective function after optimization constraints:

[0056]

[0057] Among them, η and ε are two learnable parameters used to determine the priority of the two objective functions, M is the normalization factor, and N is the number of samples. The first term is the contrast loss, which calculates the gradient of the input at different scales through the normalization transformation f(~), and applies the gradient operator B to compare the consistency of the gradient to ensure that the scale transformation does not cause excessive gradient changes, thereby improving the robustness of the model to inputs of different scales and enhancing the generalization ability. The second term is smoothing regularization, which suppresses high-frequency noise and makes the signal smoother by constraining the gradient norm. At the same time, by limiting Bb j By controlling the Laplace eigenvalue, optimizing the low-frequency characteristics of the signal, and improving the reconstructibility of the signal, the model can maintain good structural consistency and interpretability under different scales and transformation conditions.

[0058] In the design of sampling operators in image processing, the reciprocal relationship of scaling factors plays a key role. The specific design method is to set a basic scaling factor α, which represents the scaling ratio of a certain dimension of the image (such as width or height). When downsampling by this multiple, the size of the image is reduced to 1 / ɑ of the original size, thereby removing high-frequency noise and details and retaining the main structure and edge features. Then, the downsampled image is upsampled using the multiple 1 / α of the reciprocal relationship to achieve the effect of restoring to a size close to the original size. This mechanism of removing redundant information by downsampling and then restoring it by upsampling can highlight the edge information in the image without losing geometric characteristics. Through this design, more edge details can be retained during the image processing process, thereby improving the quality of the image, especially the expressiveness.

[0059] By minimizing formula (6) and applying the Lagrange multiplier rule, a low-order linear equation system is obtained. Combined with the requirement of taking the inverse relationship of the scaling factor, the designed filter can be obtained. The specific expression is as follows:

[0060]

[0061] In summary, the advantages and positive effects of the present invention are as follows: The bilinear interpolation filter proposed in this invention, through optimized design and combining multiple objectives, can effectively preserve image edge and singularity features, avoiding the loss of detail and high-frequency information during scaling. By constructing an objective function and minimizing differences, the filter ensures accurate reproduction of singularities (such as edges and corners), thereby improving image quality. In particular, it can precisely locate edges and preserve important features in edge detection and image segmentation tasks. It utilizes the principle of bilinear interpolation to remove unnecessary details and high-frequency noise through downsampling, preserving structural information, and then restore the image's size and details through upsampling. During this process, the filter also optimizes low-frequency information by controlling the low-frequency span, avoiding aliasing effects and ensuring a smoother and clearer image. Furthermore, Taylor expansion analysis ensures a multiple relationship between residual information and the first- and second-order differences of the image, thereby further extracting fine edge information, enhancing image structure, and providing accurate edge detection and feature extraction. Overall, this filter can improve image quality under different scales and transformation conditions, ensuring the integrity of edge information and optimizing the low-frequency characteristics of the image, providing high-quality results for various image processing requirements.

[0062] The technical effects of the present invention are described in detail below in combination with performance testing and experimental analysis. We conducted comparative experiments with a variety of classic methods, including the traditional Canny edge detection algorithm, and deep learning-based segmentation methods UNet, SwinUNet, TransUNet, EgeUNet, and SegmentAnything. In addition, the deep learning edge detection methods MuGE and DiffusionEdge were also compared. These methods are all implemented in the Python programming language to ensure the fairness and comparability of the experiment. In terms of performance evaluation, we use accuracy (Accuracy, Acc) and mean Intersection over Union (mIoU) to measure the segmentation accuracy and detection effect of the model, and introduce FPS (Frames Per Second) as a real-time indicator. Among them, FPS represents the number of frames that the network can process per second, Acc reflects the proportion of the number of correctly segmented pixels to the total number of pixels, and mIoU measures the average value of the intersection over Union of each category. The specific calculation formula is as follows:

[0063]

[0064] Among them, TP represents the number of instances correctly identified as positive by the model, TN represents the number of instances correctly identified as negative by the model, FP represents the number of instances that the model incorrectly predicts as positive from negative classes, and FN represents the number of instances that the model incorrectly predicts as negative from positive classes.

[0065] Table 1 Comparison of segmentation accuracy and average intersection-over-union ratio of different networks

[0066]

[0067] From the results in Table 1, it can be seen that the images enhanced by the bilinear residual filter (BRF) in this application perform well in terms of accuracy (Acc) and mean intersection over union (mIoU). Compared with traditional edge detection methods and semantic segmentation algorithms, BRF shows stronger comprehensive performance. Although the FPS of BRF is slightly lower (by 5.3%) than that of the classic Canny edge detection algorithm in terms of processing speed, the improvement in its segmentation accuracy is particularly significant. Among them, Acc is improved by 5.53% and mIoU is improved by 4.48%, indicating that it has stronger capabilities in capturing edge details and extracting contours. In addition, compared with mainstream deep learning semantic segmentation and edge detection methods, BRF can significantly improve segmentation accuracy while maintaining computational efficiency. Its bilinear residual structure enhances the ability to parse details by introducing more information flow and contextual features, thereby showing obvious advantages in key indicators such as Acc and mIoU. This feature not only improves the recognition of coal particle edges but also ensures real-time performance in practical applications, making it more practical for precise coal particle segmentation tasks in the industrial field. BRF achieves optimized segmentation accuracy without significantly sacrificing processing speed, providing reliable technical support for refined coal particle identification and segmentation.

[0068] In order to verify the performance of the model, the present invention also randomly selected five different coal samples for experiment and compared the segmentation effects of BRF with the various algorithms listed in Table 1 (such as Figure 5-7 As shown), in order to show the segmentation results more clearly, we use the blue rectangle to amplify the details of the coal particles in the red rectangle:

[0069] Figure 5 The small picture a in the figure is a schematic diagram of coal sample combination A. Figure 5 The a1 sub-graph in the figure is the result of identifying the coal sample combination A using the Canny algorithm. Figure 5 The a2 sub-graph in the figure is the result of using the UNet algorithm to identify the coal sample combination A. Figure 5 The a3 sub-graph in the figure is the result of identifying the coal sample combination A using the SwinUNet algorithm. Figure 5 The a4 sub-graph in the figure is the result of identifying the coal sample combination A using the TransUNet algorithm. Figure 5 The a5 sub-graph in the figure is the result of using the EgeUNet algorithm to identify the coal sample combination A. Figure 5 The a6 figure in the figure is the result of using the SAM algorithm to identify the coal sample combination A. Figure 5The a7 sub-graph in the figure is the result of identifying the coal sample combination A using the MuGe algorithm. Figure 5 The a8 sub-graph in the figure is the result of identifying the coal sample combination A using the DiffusionEdge algorithm. Figure 5 The a9 diagram in the figure is the result of using BRF to identify the coal sample combination A. Figure 5 The small picture a10 in the figure is the real image data of coal sample combination A;

[0070] Figure 6 The small picture b in the figure is a schematic diagram of coal sample combination B. Figure 6 The small picture b1 in the figure is the result of identifying the coal sample combination B using the Canny algorithm. Figure 6 The b2 sub-graph in the figure is the result of using the UNet algorithm to identify the coal sample combination B. Figure 6 The b3 sub-graph in the figure is the result of identifying the coal sample combination B using the SwinUNet algorithm. Figure 6 The b4 sub-graph in the figure is the result of identifying coal sample combination B using the TransUNet algorithm. Figure 6 The b5 sub-graph in the figure is the result of using EgeUNet algorithm to identify coal sample combination B. Figure 6 The small picture b6 in the figure is the result of identifying the coal sample combination B using the SAM algorithm. Figure 6 The b7 sub-graph in the figure is the result of identifying coal sample combination B using MuGe algorithm. Figure 6 The small picture b8 in the figure is the result of identifying the coal sample combination B using the DiffusionEdge algorithm. Figure 6 The b9 diagram in the figure is the result diagram of coal sample combination B identification using BRF. Figure 6 The small picture b10 in the figure is the real image data of coal sample combination B;

[0071] Figure 7 The small figure c in the figure is a schematic diagram of coal sample combination C. Figure 7 The small figure c1 in the figure is the result of identifying the coal sample combination C using the Canny algorithm. Figure 7 The small figure c2 in the figure is the result of using the UNet algorithm to identify the coal sample combination C. Figure 7 The small figure c3 in the figure is the result of using SwinUNet algorithm to identify the coal sample combination C. Figure 7 The small figure c4 in the figure is the result of identifying the coal sample combination C using the TransUNet algorithm. Figure 7 The small figure c5 in the figure is the result of using the EgeUNet algorithm to identify the coal sample combination C. Figure 7 The small figure c6 in the figure is the result of identifying the coal sample combination C using the SAM algorithm. Figure 7 The small figure c7 in the figure is the result of identifying the coal sample combination C using the MuGe algorithm. Figure 7The small figure c8 in the figure is the result of identifying the coal sample combination C using the DiffusionEdge algorithm. Figure 7 The small figure c9 in the figure is the result of using BRF to identify the coal sample combination C. Figure 7 The small picture c10 in the figure is the real image data of coal sample combination C.

[0072] Experimental results show that the traditional Canny edge detection algorithm suffers from incomplete contour detection and jagged edges, while UNet and its derivative semantic segmentation algorithms, SwinUNet, TransUNet, and EgeUNet, cause severe deformation of coal particle shapes during the segmentation process. Furthermore, the SegmentAnything Model (SAM) is prone to missed segmentations when processing small coal particles, while the diffusion model-based DiffusionEdge still has some shortcomings in terms of coal particle contour integrity. In contrast, the MuGe algorithm performs relatively well in detecting coal particle contours, but still suffers from jagged edges and positional deviations compared to GT (ground truth). Comprehensive analysis shows that BRF excels in coal particle edge integrity, reducing missed segmentations, and preserving shape, with the detected coal particle contours being closest to GT. Compared to other algorithms, BRF achieves significant improvements in segmentation accuracy and preservation of edge details, further demonstrating its superiority in the task of accurate coal particle segmentation.

[0073] The bilinear residual filter in this application is used to segment the 27 coal particle images to ensure the accurate extraction of coal particle size features. At the same time, the segmented coal particle images are analyzed using the equivalent circle particle size measurement method to obtain the particle size of each coal particle, and the actual coal particle size distribution histogram and the particle size distribution histogram based on the equivalent circle particle size measurement are plotted, as shown in Figure 2. Figure 8 As shown:

[0074] Figure 8 In the a and b graphs, the horizontal axis represents the average particle size. Figure 8 The small figure a is the actual particle size of the real coal particles, and the small figure b is the particle size measurement result of the BRF-segmented coal particles using the equivalent circle particle size measurement method. According to the measurement results, the coal particle size is divided into 12 intervals. Among them, since most coal particles are larger than 1mm in size, the first interval is set to 0-1mm, and the intervals of the remaining intervals are 0.2mm. The left vertical axis represents the number of coal particles in each interval, and the blue and green bar graphs respectively show the number of particles in each interval; the right vertical axis represents the cumulative distribution, and the red curve shows the cumulative distribution trend. It is observed that the coal particle size distribution shows a trend close to the normal distribution, with a prominent peak in the middle and gradually decreasing on both sides, forming a typical "high in the middle and low at both ends" distribution pattern. This shows that the coal particle size is relatively evenly distributed in the range of 1-3mm, and the measurement results have good stability.

[0075] With the above-described preferred embodiments of the present invention as a guide, and with reference to the above description, relevant personnel are fully capable of making various changes and modifications without departing from the technical spirit of this invention. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for constructing a bilinear residual filter for use in coal powder particle measurement, characterized in that: The following steps are included: Step 1: Based on the basic principle of bilinear interpolation, a scaling operator B is inserted to design a bilinear residual unit in the bilinear residual filter; Step 2: From a mathematical perspective, the filter is optimized by Taylor expansion and combined with the optimization objective function; Step 3: Design the sampling operator so that the scaling operator can meet the low-frequency span requirement during the sampling process; Step 4: Consider the inverse relationship between the scaling factors to obtain the final optimized bilinear residual filter.

2. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 1, characterized in that: In the step 1, the bilinear residual filter has a bilinear residual unit, which includes an upsampler, a downsampler and a subtractor, wherein the scaling operator B is used as a structural component of the bilinear residual unit for upsampling and downsampling of the image.

3. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 2, characterized in that: The scaling operator B satisfies the characteristic of uniform scaling in space, defining the linear mapping function where x′∈G i ,i∈1,2,…, α is the scale factor, then B should satisfy:

4. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 1, characterized in that: In the step 2, the Gaussian function is used To simulate the singularity features, and consider all possible offsets and scale changes by stretching the sub-pixel offset μ and the standard deviation σ; by minimizing the distance between the downsampled Gaussian function f and the ideal or expected Gaussian function f, the singularity features are accurately preserved.

5. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 4, characterized in that: In the second step, the objective function is designed Where M is the normalization factor, which is equal to the number of summation terms; μ is the mean; and σ is the standard deviation.

6. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 5, characterized in that: In step 2, based on the linear characteristics of the filter, the residual layer E(x) used to represent the edge contour is expressed as E(x)=a×I(x)+b, where a and b are known constants. Taylor expansion at any point x0 can be obtained: in, Available 7. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 1, characterized in that: In step 3, a new objective function is defined for the low-frequency span: Where B is the discrete differential operator, b j is the input signal.

8. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 7, characterized in that: In step 4, the objective function after optimization constraint is obtained by combining the objective functions in steps 2 and 3. Among them, η and ε are two learnable parameters used to determine the priority of the two objective functions, M is the normalization factor, and N is the number of samples.

9. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 8, characterized in that: In step 4, a basic scaling factor α is defined to represent the scaling ratio of a certain dimension of the image (such as width or height). When downsampling is performed using this factor, the size of the image is reduced to 1 / α of the original size. The downsampled image is upsampled using the reciprocal factor 1 / α to achieve the effect of restoring the image to a size close to the original size.

10. The method for constructing a bilinear residual filter for use in coal powder particle measurement according to claim 9, characterized in that: In step 4, the Lagrange multiplier rule is applied based on the objective function after optimization constraint, combined with the reciprocal relationship of the scaling factor, to obtain the final optimized bilinear residual filter minL

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