Construction method of bilinear residual filter applied in coal particle measurement

Abstract

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

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of image enhancement recognition, and particularly relates to a construction method of a bilinear residual filter applied in coal dust particle measurement. BACKGROUND

[0002] In recent years, the state has continuously improved the degree of attention to the field of coal mine safety, and the safety situation of coal mines has been improved, but accidents still occur from time to time, which shows that safety challenges still exist. In the mining, transportation and crushing processes of coal mines, the release of gas and coal particles is a common phenomenon, and the amount of release varies with the operation link. The occurrence of gas explosion is mainly caused by the wide distribution of methane gas in the coal mine, and the size characteristics of coal particles play a crucial role therein. The particle size of coal particles directly affects the diffusion mode, accumulation state and propagation path of methane, and also affects the behavior characteristics of methane in the adsorption, diffusion and emission processes. These differences in characteristics provide a theoretical basis for in-depth research and prediction of the activity law of methane in coal mines. It is worth noting that coal particles with a particle size less than 75 microns pose a serious safety threat due to their extremely high explosion sensitivity. Therefore, it is of important academic and practical significance to analyze the particle size distribution of coal particles using a high-precision detection method to evaluate the effect of dust prevention facilities in coal mines and improve the safety protection level of the operation site.

[0003] With the development of image processing technology and the application of deep learning technology in image processing, image analysis has made significant progress in the field of particle detection and segmentation. However, although deep learning methods have shown high efficiency and accuracy in coal particle segmentation, they still face some challenges. In the coal mine operation environment, the image recognition accuracy is poor, and the recognition quality of target edge features is low, which cannot effectively cope with the complexity and fine-grained measurement requirements of coal dust particles. SUMMARY

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

[0005] To this end, the present application provides a construction method of a bilinear residual filter applied in coal dust particle measurement, which efficiently performs image up-sampling and down-sampling, 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 application to solve the technical problem is:

[0007] A construction method of a bilinear residual filter applied in coal dust particle measurement, comprising the following steps,

[0008] Step one, based on the basic principle of bilinear interpolation, insert the scaling operator B to design the bilinear residual unit in the bilinear residual filter;

[0009] Step two, from the mathematical point of view, build and optimize the filter by combining the optimization objective function through Taylor expansion;

[0010] Step three, design the sampling operator to make the scaling operator meet the low frequency span requirement in the sampling process;

[0011] Step four, considering the reciprocal relationship between the scaling factors, get the final optimized bilinear residual filter.

[0012] Further, in the step one, the bilinear residual filter has a bilinear residual unit, the bilinear residual unit includes an up-sampler, a down-sampler and a subtractor, wherein the scaling operator B is used as a structural component of the bilinear residual unit for the up-sampling and down-sampling of the image.

[0013] Further, the scaling operator B meets the characteristics of uniform scaling in space, and defines a linear mapping function Where x' ∈ G i ,i∈1,2,…,α is the scale factor, then B should meet:

[0014] Further, in the step two, a Gaussian function Is used to simulate the singularity feature, and all possible offset and scale changes are considered by the sub-pixel offset μ and the stretching of the standard deviation σ; by minimizing the distance between the down-sampled Gaussian function f and the ideal or desired Gaussian function f, the accurate preservation of the singularity feature is realized.

[0015] Further, in the step two, the objective function Is designed, wherein M is a normalization factor, equal to the number of summation terms; μ represents the mean; σ represents the standard deviation.

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

[0017] Further, in step three, a new objective function is defined for low frequency span: Wherein, B is a discrete differential operator, b j Is the input signal.

[0018] Further, in the step four, the target function in the step two and the step three is combined to obtain the target function after optimization constraint Wherein, η and ε are two learnable parameters for determining the priority of the two target functions, M is a normalization factor, and N is the number of samples.

[0019] Further, in the step four, a basic scaling multiple α is defined to represent the scaling ratio of a certain dimension (such as width or height) of the image, and when downsampling is performed through the multiple, the size of the image is reduced to 1 / α of the original size. The inverse relationship multiple 1 / α is used to upsample the downsampled image to restore the size close to the original size.

[0020] Further, in the step four, the Lagrange multiplier rule is applied to obtain the final optimized bilinear residual filter based on the target function after optimization constraint and the inverse relationship of the scaling multiple

[0021] The application has the beneficial effects that, based on the basic principle of bilinear interpolation, the bilinear residual unit in the bilinear residual filter is optimized and designed to ensure that key detail information can be effectively preserved during image scaling and loss of high-frequency information caused by interpolation is reduced. At the same time, combined with the extraction and compensation mechanism of residual information, the ability of the filter to maintain edge features is enhanced, thereby improving the quality and segmentation accuracy of the scaled image. On this basis, the target function is further constructed and optimized to enable the scaling operator to accurately maintain the singular point features in the image. Through reasonable mathematical modeling and constraint conditions, it is ensured that the filter can accurately capture edge features at different scales and avoid the problems of edge blur or information loss during image scaling. Then, a suitable sampling operator is designed to ensure that the sampling process of the scaling operator meets the low-frequency span requirement. In this process, the bandwidth constraint and frequency domain characteristics are fully considered to enable the filter to effectively suppress aliasing effects during upsampling and downsampling, thereby improving the reconstruction quality and visual consistency of the image. Finally, considering the inverse relationship between the scaling multiples and combining the aforementioned optimization designs, the bilinear residual filter satisfying the linearity invariance, low-frequency span control and singular point maintenance characteristics is finally obtained. The filter not only accurately restores edge details during image scaling, but also maintains stable segmentation performance in complex environments, providing a better solution for image processing, target detection and coal particle size measurement applications. BRIEF DESCRIPTION OF DRAWINGS

[0022] The application will be further described below in conjunction with the drawings and examples.

[0023] Figure 1 is a flowchart of the construction method of the bilinear residual filter applied in the coal particle size measurement in the application.

[0024] Figure 2 This is a block diagram of the construction method of the bilinear residual filter in this invention.

[0025] Figure 3 This is a schematic diagram of the bilinear interpolation algorithm in this invention.

[0026] Figure 4 This is a schematic diagram of the basic unit of the bilinear residual filter in this invention.

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

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

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

[0030] Figure 8 This is a schematic diagram showing the results of coal particle size measurement using image enhancement identification with the bilinear residual filter described in this application. Detailed Implementation

[0031] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0032] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, features defined with "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0033] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0034] A method for constructing a bilinear residual filter for use in coal powder particle measurement, including...

[0035] Bilinear interpolation is a common image processing algorithm widely used to solve the problem of estimating unknown pixel values ​​between two-dimensional data points. Its core idea is to perform linear interpolation twice, in the horizontal and vertical directions respectively, to generate a smoother, more natural transition effect. Specifically, when the target pixel's coordinates lie between four known pixels (forming a 2×2 pixel block), first, linear interpolation is performed on two adjacent pixels in the horizontal direction to calculate two intermediate values; then, linear interpolation is performed again on these two intermediate values ​​in the vertical direction to deduce 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 the x and y directions. Assume Q... 11 Q 12 Q 21 Q 22 To determine the positions of the four pixels required for scaling, Q 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 result of the bilinear interpolation calculation is as follows:

[0037]

[0038] The bilinear residual unit is the basic structure of a bilinear residual filter. Just as... Figure 4 As shown, it consists of three parts: a bilinear upsampler, a bilinear downsampler, and a subtractor. Figure 4 In the diagram, blue, yellow, and green rectangular blocks are used to represent the edges of the image. Based on the characteristics of signal transmission, a 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 +f(Q 11 )*ω 12 = KX + b, where ω 21 , ω 22 , ω 11 , ω 11 are the weights of the four determined points, the matrix composed of K, X, and b is respectively, wherein X is a matrix composed of four f(*) values, b is a bias matrix to prevent being 0, and f(x, y) = Q 21 *ω 21 + Q 12 *ω 12 + Q 22 *ω 22 = KX + b is denoted as B, and E(x) = I(x) - B(B(I(x))) is obtained, which is E = I - K'(KI + b) + b' = (I - K'(K)I - K'(b) + b', which satisfies the linear property. T T

[0040] Because the bilinear residual unit satisfies the linear property, the scaling operator B, as a structural component of the bilinear residual unit, is used for image up-sampling and down-sampling, so the scaling operator B should also satisfy the characteristics of uniform scaling in space, that is, the low-resolution image or feature map P l+1 is linearly mapped to the high-resolution image I l , or the pixel of the high-resolution image I l or the low-resolution image or feature map P l+1 by a linear function. Based on this, the linear mapping function is defined as where x' ∈ G i , i ∈ 1, 2, …, and α is a scale factor, the value of which is not fixed, then B should satisfy the following expression:

[0041]

[0042] where x' is the pixel position of the scaled image, x is the pixel position of the original image obtained through the linear mapping relationship, and x o obtained by the above formula is the pixel value obtained by B operator at the position of the pixel point x' in the original image mapping. ​​

[0043] Step two, construct and optimize the objective function to enable the scaling operator in the filter to accurately preserve the singularity features in the image.

[0044] During the image sampling process, part of the high-frequency information and the singularities in the image (such as edge and corner features) are inevitably lost. These high-frequency information is crucial for the details of the image and feature recognition, and its absence often leads to a decline in image quality and blurred feature information. Therefore, when designing the sampling operator, it is necessary to fully consider how to maximize the preservation of these key information, especially to ensure that the morphology of singularities remains consistent. For this purpose, a Gaussian function is used to simulate the singularity features, and all possible shifts and scale changes are considered through the sub-pixel shift μ and the stretching of the standard deviation σ. Finally, by minimizing the distance between the down-sampled Gaussian function f and the ideal or desired f, the accurate preservation of the singularity features is achieved. This optimization process constructs an objective function to ensure the effective preservation of important information during the scale transformation, so that even after multiple up-sampling or down-sampling, 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, equal to the number of summation terms; μ represents the mean; σ represents the standard deviation.

[0047] As shown in the above step, the designed filter is linear, so Figure 4 E(x) and I(x) in are linearly related, so E(x) = a x I(x) + b, a, b are known constants. Taylor expansion of this formula at any point x0 can be obtained as follows: where x - x0 is very small, so Where, a, b, g are adjustable linear relationship coefficients respectively. From this formula, it can be seen that the obtained residual information and the first-order difference and second-order difference of the input signal have a multiple relationship. The first-order difference is mainly used to extract the rough edge information of the image, outline the overall contour and basic shape features of the target, and provide clear visual guidance in complex scenes, which is crucial for image structure recognition. In contrast, the second-order difference focuses more on the extraction of fine edges, which can accurately locate the corner points and small details, making the edge detection more refined. This accurate edge information extraction is particularly crucial in image segmentation tasks, as it can reveal the subtle changes in the image and ensure the complete capture of complex shape and texture information. In summary, the designed bilinear residual filter not only has excellent edge-preserving performance, but also effectively maintains important edge features during scaling or resampling, and has strong adaptability. Through the comprehensive use of first-order and second-order differences, the filter can optimize the image processing effect at different levels, making the edge detection more accurate, thereby providing strong support for high-quality image segmentation and feature extraction.

[0048] In the scaling process, the optimization objective function we constructed follows the singularity preservation principle, ensuring that key features such as edges and corners will not be lost or distorted due to scaling. Then, from a mathematical perspective, the Taylor expansion is used to derive the multiple relationship between the residual information and the first-order and second-order differences, ensuring the correct mapping relationship of singularities at different scales. Therefore, the filter maintains the overall edge profile, achieving the effect of edge preservation.

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

[0050] The Point Spread Function (PSF) and the anti-aliasing filter built-in the camera play a crucial role in the image processing procedure. These filters restrict the bandwidth of the input signal (i.e. the scene) according to the sampling rate of the sensor to ensure that the signal satisfies or approximately satisfies the Nyquist sampling theorem, thus affecting the up-sampling and down-sampling processes of the image. In the up-sampling process, although the filter has limited the bandwidth of the original signal, making the up-sampled image have a certain improvement in resolution, the actual detail enhancement is still limited due to the restriction of the increase in detail information by the original signal bandwidth. Therefore, although the image may appear clearer visually, the essential information richness has not been significantly improved. In contrast, in the down-sampling process, the filter plays a more crucial role, as it can effectively remove high-frequency components that exceed the sampling rate range of the sensor, avoiding artifacts caused by aliasing effects, thus ensuring that the down-sampled image remains clear. As can be seen, when designing the sampling operator, it is necessary to ensure that the sampling process reasonably preserves the low-frequency signal to optimize image quality. Here, "low-frequency span" refers to the proportion or range of low-frequency components in the image signal, which is one of the important factors affecting image quality. Precise control of the low-frequency span helps to optimize sampling efficiency, enabling the image to maintain high clarity and rich details under different operating conditions.

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

[0052]

[0053] where B is the discrete differential operator, b j is the input signal sample, and 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 details), while low-frequency components represent the overall structure or smooth parts of the signal. The discrete differential operator B, when acting on the signal in the spatial (time) domain, is equivalent to applying a high-pass filter in the frequency domain. Therefore, it is actually controlling the eigenvalue distribution of the Laplacian matrix, suppressing high-frequency components to enhance the expressiveness of low-frequency components, making the signal smoother and more reconstructable.

[0054] Step four, considering the reciprocal relationship between the scaling factors and combining the optimization design of the previous steps, we finally obtain a bilinear residual filter that satisfies the linearity invariance, low-frequency span control, and singularity preservation characteristics.

[0055] Combining the objective functions proposed in the first two steps, we obtain the following optimized objective function:

[0056]

[0057] where η and ε are two learnable parameters to determine the priority of two objective functions, M is a normalization factor, and N is the number of samples. The first term is the contrastive loss, which calculates the gradient of the input at different scales through a standardization transformation f(~), and applies the gradient operator B to compare the consistency of the gradient, ensuring that the scale transformation does not cause excessive gradient changes, thereby improving the robustness of the model to different scale inputs and enhancing the generalization ability. The second term is the smooth regularization, which suppresses high-frequency noise by constraining the gradient norm, making the signal smoother, and at the same time, limits the change of the gradient norm by Bb j Control the eigenvalue of Laplacian, optimize the low-frequency characteristics of the signal, improve the reconfigurability of the signal, and make the model still maintain good structural consistency and interpretability under different scale 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 through this factor, the size of the image is reduced to 1 / ɑ of the original size, thereby removing high-frequency noise and details and preserving the main structure and edge features. Then, use the reciprocal relationship of the factor 1 / α to upsample the downsampled image to restore the original size. This mechanism of removing redundant information through downsampling and then restoring through upsampling can highlight the edge information in the image without losing geometric characteristics. Through this design, more edge details can be preserved in the image processing process, thereby improving the quality of the image, especially the expressiveness.

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

[0060]

[0061] In summary, the advantages and positive effects of the present application are: the bilinear interpolation filter proposed in the present application can effectively maintain the edge and singularity characteristics of the image by optimizing the design and combining multiple objectives, avoiding the loss of details and high-frequency information during scaling. The filter ensures the accurate reproduction of singularities (such as edges, corners, etc.) by constructing an objective function and minimizing the difference, thereby improving the image quality, especially in edge detection and image segmentation tasks, which can accurately locate the edges and maintain important features. It adopts the principle of bilinear interpolation, removes unnecessary details and high-frequency noise through downsampling, preserves structural information, and then restores the size and details of the image through upsampling. In this process, the filter also controls the low-frequency span, optimizes the low-frequency information, avoids aliasing effects, and ensures that the image is smoother and clearer. At the same time, Taylor expansion analysis ensures the multiple relationship between residual information and 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, ensure the integrity of edge information, and optimize the low-frequency characteristics of the image, providing high-quality results for various image processing needs.

[0062] The technical effects of the present application will be described in detail below in combination with performance tests and experimental analysis. We conducted comparative experiments with various classical methods, including the traditional Canny edge detection algorithm, and the segmentation methods UNet, SwinUNet, TransUNet, EgeUNet, SegmentAnything based on deep learning. In addition, we also compared the deep learning edge detection methods MuGE and DiffusionEdge. These methods are all implemented based on the Python programming language to ensure the fairness and comparability of the experiments. In terms of performance evaluation, we use accuracy (Accuracy, Acc) and mean Intersection over Union (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 correctly segmented pixel numbers to the total pixel numbers, and mIoU measures the average value of the Intersection over Union of each class. 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 incorrectly predicted as positive by the model, and FN represents the number of instances incorrectly predicted as negative by the model.

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

[0066]

[0067] As shown in Table 1, the image enhancement processed by the bilinear residual filter (BRF) in this application exhibits superior performance in both accuracy (Acc) and mean intersection-over-union (mIoU). Compared to traditional edge detection methods and semantic segmentation algorithms, BRF demonstrates stronger overall performance. Although the processing speed of BRF is slightly lower (by 5.3%) compared to the classic Canny edge detection algorithm, its improvement in segmentation accuracy is particularly significant. Specifically, Acc is improved by 5.53%, and mIoU by 4.48%, indicating its stronger ability to capture edge details and extract contours. Furthermore, compared to 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 resolve details by introducing more information flow and contextual features, thus demonstrating a clear advantage in key metrics 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 valuable for precise coal particle segmentation in industrial settings. BRF achieves optimized segmentation accuracy without significantly sacrificing processing speed, providing reliable technical support for refined coal particle identification and segmentation.

[0068] To verify the model's performance, this invention also randomly selected five different coal samples for experiments and compared the segmentation effects of BRF with those of various algorithms listed in Table 1 (e.g., Figures 5-7 As shown in the image, to more clearly demonstrate the segmentation results, we have used a blue rectangle to magnify the details of the coal particles within the red rectangle:

[0069] Figure 5 The small figure 'a' in the diagram is a schematic diagram of coal sample combination A. Figure 5 The small image a1 in the image shows the result of identifying coal sample combination A using the Canny algorithm. Figure 5 The small image a2 in the image shows the result of identifying coal sample combination A using the UNet algorithm. Figure 5 The small image a3 in the image shows the result of identifying coal sample combination A using the SwinUNet algorithm. Figure 5 The small image a4 in the image shows the result of identifying coal sample combination A using the TransUNet algorithm. Figure 5 The small image a5 in the image shows the result of identifying coal sample combination A using the EgeUNet algorithm. Figure 5 The small image a6 in the figure shows the result of identifying coal sample combination A using the SAM algorithm. Figure 5a7 in FIG. 1 is a result image of the coal sample combination A identified by using the MuGe algorithm, Figure 5 a8 in FIG. 1 is a result image of the coal sample combination A identified by using the DiffusionEdge algorithm, Figure 5 a9 in FIG. 1 is a result image of the coal sample combination A identified by using the BRF, Figure 5 a10 in FIG. 1 is a real image data of the coal sample combination A;

[0070] Figure 6 b in FIG. 2 is a schematic diagram of the coal sample combination B, Figure 6 b1 in FIG. 2 is a result image of the coal sample combination B identified by using the Canny algorithm, Figure 6 b2 in FIG. 2 is a result image of the coal sample combination B identified by using the UNet algorithm, Figure 6 b3 in FIG. 2 is a result image of the coal sample combination B identified by using the SwinUNet algorithm, Figure 6 b4 in FIG. 2 is a result image of the coal sample combination B identified by using the TransUNet algorithm, Figure 6 b5 in FIG. 2 is a result image of the coal sample combination B identified by using the EgeUNet algorithm, Figure 6 b6 in FIG. 2 is a result image of the coal sample combination B identified by using the SAM algorithm, Figure 6 b7 in FIG. 2 is a result image of the coal sample combination B identified by using the MuGe algorithm, Figure 6 b8 in FIG. 2 is a result image of the coal sample combination B identified by using the DiffusionEdge algorithm, Figure 6 b9 in FIG. 2 is a result image of the coal sample combination B identified by using the BRF, Figure 6 b10 in FIG. 2 is a real image data of the coal sample combination B;

[0071] Figure 7 c in FIG. 3 is a schematic diagram of the coal sample combination C, Figure 7 c1 in FIG. 3 is a result image of the coal sample combination C identified by using the Canny algorithm, Figure 7 c2 in FIG. 3 is a result image of the coal sample combination C identified by using the UNet algorithm, Figure 7 c3 in FIG. 3 is a result image of the coal sample combination C identified by using the SwinUNet algorithm, Figure 7 c4 in FIG. 3 is a result image of the coal sample combination C identified by using the TransUNet algorithm, Figure 7 c5 in FIG. 3 is a result image of the coal sample combination C identified by using the EgeUNet algorithm, Figure 7 c6 in FIG. 3 is a result image of the coal sample combination C identified by using the SAM algorithm, Figure 7 c7 in FIG. 3 is a result image of the coal sample combination C identified by using the MuGe algorithm, Figure 7The small image c8 in the image shows the result of identifying coal sample combination C using the DiffusionEdge algorithm. Figure 7 The small image c9 in the figure shows the results of identifying coal sample combination C using BRF. Figure 8 The c10 small image in the image is the actual image data of coal sample combination C.

[0072] Experimental results show that traditional Canny edge detection algorithms suffer 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 segmentation. Furthermore, the SegmentAnything Model (SAM) is prone to missing segments when processing small coal particles, while DiffusionEdge, based on a diffusion model, still has some shortcomings in terms of coal particle contour integrity. In contrast, the MuGe algorithm performs relatively well in coal particle contour detection, but compared to ground truth (GT), it still suffers from jagged edges and positional deviations. Comprehensive analysis shows that BRF performs excellently in terms of coal particle edge integrity, reducing missed segments, and shape preservation, with the detected coal particle contours being closest to GT. Compared to other algorithms, BRF achieves significant improvements in segmentation accuracy and edge detail preservation, further demonstrating its superiority in accurate coal particle segmentation.

[0073] The bilinear residual filter described in this application is used to segment 27 coal particle images to ensure accurate extraction of coal particle size features. Simultaneously, the equivalent circular particle size measurement method is used to analyze the segmented coal particle images, obtain the particle size of each coal particle, and plot both the actual coal particle size distribution histogram and the particle size distribution histogram based on the equivalent circular particle size measurement. Figure 8 As shown:

[0074] Figure 8 In the subplots a and b, the horizontal axis represents the average particle size. ​ In the figure, small image a shows the actual particle size of the coal particles, and small image b shows the particle size measurement results of the coal particles segmented by BRF using the equivalent spherical particle size measurement method. Based on the measurement results, the coal particle size is divided into 12 intervals. Since most coal particles are larger than 1 mm, the first interval is set to 0-1 mm, and the intervals for the remaining intervals are 0.2 mm apart. The left vertical axis represents the number of coal particles in each interval, with blue and green bars showing the number of particles in each interval, respectively. The right vertical axis represents the cumulative distribution, with the red curve showing the cumulative distribution trend. It is observed that the coal particle size distribution shows a near-normal distribution trend, with a prominent peak in the middle and a gradual decrease at both ends, forming a typical "high in the middle, low at both ends" distribution pattern. This indicates that the coal particle size distribution is relatively balanced within the 1-3 mm range, and the measurement results have good stability.

[0075] The above-described embodiments according to the present application are intended to be illustrative only. Changes can be made by those skilled in the art, without departing from the scope of the present application, which is set out in the claims. The technical scope of the present application is not limited to the above-described embodiments. The technical scope of the present application must be determined by the claims.

Claims

1. A method for constructing a bilinear residual filter for use in coal powder particle measurement, characterized in that, Includes the following steps, Step 1: Based on the basic principle of bilinear interpolation, the bilinear residual unit in the bilinear residual filter is designed by inserting the scaling operator B. Step two: From a mathematical perspective, construct and optimize the filter using Taylor expansion and the objective function. Step 3: Design the sampling operator so that the scaling operator meets the low-frequency span requirement during the sampling process; Step four: Consider the reciprocal relationship between the scaling factors to obtain the final optimized bilinear residual filter; In step one, the bilinear residual filter has a bilinear residual unit, which includes an upsampler, an downsampler, and a subtractor. The scaling operator B is used as a structural component of the bilinear residual unit for upsampling and downsampling of the image. The scaling operator B satisfies the characteristic of uniform scaling in space, and a linear mapping function is defined. ,in , If it is a scaling factor, then It should meet the following requirements: ,in, To the pixel position in the scaled image, The pixel position in the original image is obtained through a linear mapping relationship. In order to be in The location of this pixel is mapped from the original image. The pixel value obtained by the operator; In step two, a Gaussian function is used. To simulate singularity features, and through sub-pixel offset and the standard deviation The stretching is used to account for all possible offsets and scale variations; this is achieved by minimizing the Gaussian function after downsampling. f With the ideal or expected Gaussian function f The distance between them enables precise preservation of singularity features; In step two, the objective function is designed. , where M is the normalization factor, which is equal to the number of terms in the summation; This represents the mean; Indicates standard deviation; In step three, a new objective function is defined for low-frequency spans: Where B is the discrete differential operator, b j This is the input signal.

2. The method for constructing a bilinear residual filter for coal powder particle measurement according to claim 1, characterized in that, In step two, 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 , a , b It is a known constant, at any point Taylor expansion yields: ,in, , can be obtained .

3. The method for constructing a bilinear residual filter for coal powder particle measurement according to claim 1, characterized in that, In step four, the objective functions from steps two and three are combined to obtain the objective function after optimization constraints. ,in, and Here 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.

4. The method for constructing a bilinear residual filter for coal powder particle measurement according to claim 3, characterized in that, In step four, a basic scaling factor is defined. This represents the scaling factor of an image in a certain dimension. When downsampling is performed using this factor, the image size is reduced to 1 / 3 of its original size. Using the multiples of the reciprocal relationship 1 / Upsampling is performed on the downsampled image to restore it to a size close to the original.

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

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