Concrete member surface defect detection method and system based on image segmentation

By using frequency domain analysis and Gaussian weight fusion, the problem of insufficient adaptability of the gray-level co-occurrence matrix algorithm to multi-scale textures on concrete component surfaces is solved, achieving high-precision defect detection and generating continuous and complete defect masks.

CN121280435AActive Publication Date: 2026-01-06SHAANXI ZHONGGU XINGAN INTELLIGENT MANUFACTURING CO LTD

Patent Information

Application Number
CN202511841846.2
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-12-09
Publication Date
2026-01-06
Estimated Expiration
2045-12-09

AI Technical Summary

Technical Problem

In existing technologies, the gray-scale co-occurrence matrix algorithm cannot adapt to multi-scale textures in the detection of surface defects in concrete components, resulting in high false detection and false negative rates, while the traditional K-means clustering has poor performance.

Method used

The feature frequencies and feature spatial periods of image patches are calculated by frequency domain transformation. Gaussian weights are constructed to adaptively weight and fuse the texture features of the gray-level co-occurrence matrix. Combined with the K-means clustering algorithm, accurate differentiation of multi-scale texture features is achieved.

Benefits of technology

It significantly improves the accuracy of surface defect detection in concrete components, reduces false detection and false negative rates, and generates more continuous and complete defect masks.

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Abstract

The invention relates to the technical field of image processing, in particular to a concrete member surface defect detection method and system based on image segmentation, and the method comprises the steps: obtaining a surface image of a concrete member, and dividing the surface image into a plurality of image blocks; and performing frequency domain transformation on any image block to obtain a power spectrum. According to the method, the feature space period of each image block is analyzed and calculated through frequency domain transformation, and adaptive weighted fusion is carried out on texture features at different distances by using Gaussian weight on the basis of the feature space period. According to the method, the feature extraction process can dynamically adapt to the physical scale of image local textures, namely, small distance analysis is automatically emphasized on fine textures and large distance analysis is automatically emphasized on rough defects, so that scale-perceived composite texture features are constructed; and the accuracy of identifying the concrete surface defects under the complex texture background is obviously improved.
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Description

Technical Field

[0001] This invention relates to the field of image processing technology. More specifically, this invention relates to a method and system for detecting surface defects in concrete components based on image segmentation. Background Technology

[0002] In the automated production of precast concrete components, such as composite slabs and wall panels, surface quality inspection is a crucial quality control step to ensure product qualification rates. Common surface defects include cracks, chipped corners, honeycombing, and pitting. Among these, honeycombing and pitting defects are caused by insufficient compaction of the concrete during pouring, leading to mortar loss and voids between aggregates. These defects not only affect the appearance of the components but also reduce their structural strength and durability, making them types of defects that must be rigorously screened.

[0003] Currently, machine vision-based inspection methods are gradually replacing traditional manual visual inspection. A mainstream technical approach is to automatically extract defect regions using image segmentation algorithms. However, the surface of concrete components is not smooth and homogeneous; it is composed of cement mortar and aggregates of different particle sizes, resulting in a highly complex and uneven natural texture. In images, honeycomb and pitted defects (manifested as small-scale holes and shadows) are visually highly similar to normal aggregate textures (manifested as rough graininess and grayscale abrupt changes). Both are complex texture regions, posing a significant challenge to traditional segmentation algorithms. To address the segmentation challenge of such complex texture regions, existing technologies often employ a method combining gray-level co-occurrence matrix (GLCM) and K-means clustering. This method divides the image into multiple patches, calculates a set of texture features (such as contrast, energy, homogeneity, etc.) for each patch, and then uses the K-means clustering algorithm in this feature space, rather than the original pixel space, to classify the patches into two categories: normal texture and defect texture.

[0004] However, the standard gray-level co-occurrence matrix algorithm relies on a fixed distance parameter during calculation. Yet, the texture scale of concrete component surfaces is complex and variable: normal aggregates may exhibit fine, dense textures (high spatial frequency), while honeycomb defects may appear as large, sparse pore structures (low spatial frequency). Using a single fixed distance is a one-size-fits-all approach, failing to simultaneously capture these two different scales of texture features, resulting in insufficient discriminative power in the extracted texture features. For example, a fixed d=1 might well describe fine aggregates but fail to reflect the macroscopic structure of honeycomb pores; while a fixed d=7 might capture honeycomb features but lose the texture details of fine aggregates. Ultimately, these two distinct regions become ambiguous in the feature space, leading to poor K-means clustering results and high false positive and false negative rates. Summary of the Invention

[0005] This invention provides a method and system for detecting surface defects in concrete components based on image segmentation, aiming to solve the problem that the gray-level co-occurrence matrix in related technologies has a single scale and cannot adapt to the multi-scale texture of concrete surfaces.

[0006] In a first aspect, the present invention provides a method for detecting surface defects in concrete components based on image segmentation, comprising: acquiring a surface image of a concrete component and dividing the surface image into multiple image patches; performing a frequency domain transformation on any image patch to obtain a power spectrum; calculating the sum of the products of frequencies and energy values ​​at all non-zero frequency domain coordinates in the power spectrum and dividing it by the sum of the energy values ​​at all non-zero frequency domain coordinates to obtain the feature frequency of the image patch; using the product of the reciprocal of the feature frequency and a calibration coefficient as the feature space period of the image patch; pre-setting a gray-level co-occurrence matrix distance calculation set containing multiple fixed distance values; calculating the Gaussian weight of the image patch for each fixed distance value in the gray-level co-occurrence matrix distance calculation set according to the feature space period; and performing weighted fusion on the multi-scale texture features extracted at each fixed distance value to construct a scale-aware composite texture feature of the image patch; and using a K-means clustering algorithm to perform cluster analysis on the multiple image patches based on the scale-aware composite texture feature to distinguish them into defect patches and normal patches, thereby realizing the detection of surface defects in concrete components. The feature space period of each image patch is calculated by means of frequency domain power spectrum, and Gaussian weights are constructed to adaptively weight and fuse multi-distance GLCM features. This "patch-specific" dynamic weighting mechanism enables accurate representation of textures with different coarseness and fineness, and significantly improves the accuracy of concrete defect detection in complex backgrounds.

[0007] Furthermore, the formula for calculating the period of the characteristic space is: In the formula, Indicates the first The feature space period of an image patch For calibration coefficients, Indicates the first The feature frequencies of each image patch were established. A quantitative relationship between the frequency energy distribution and the actual physical size of the texture was established, ensuring that the subsequent Gaussian weighted calculation has a clear physical meaning. This enables the algorithm to accurately measure the coarseness of the current patch texture and provides an accurate scale benchmark for adaptive feature fusion.

[0008] Furthermore, the formula for calculating the feature frequencies of image patches is as follows: In the formula, Indicates the first Feature frequencies of image patches Represents frequency domain coordinates, Indicates coordinates The power spectral energy value at that location, Representing radial frequency. Utilizing the high robustness of frequency domain analysis, it accurately distinguishes between fine aggregate regions with concentrated high-frequency energy and honeycomb-like textured regions with concentrated low-frequency energy. Even under uneven lighting or rough surface conditions, it can stably extract frequency features reflecting the essence of the texture, providing reliable data support for scale determination.

[0009] Furthermore, the Gaussian weight of each fixed distance value in the distance set is calculated using the following formula: In the formula, Indicates the first The image patch is at a distance Gaussian weights; For the first The feature space period of an image patch; This is the scale tolerance, specifically the standard deviation of the Gaussian kernel. It mathematically simulates the degree of matching between the preset computational distance and the actual texture scale. High weights are assigned when the preset distance is close to the feature space period, and vice versa. This mechanism automatically selects the distance parameter that best characterizes the texture of the current tile, effectively suppressing feature noise caused by mismatched scales.

[0010] Furthermore, the construction of the scale-aware composite texture features includes: normalizing the Gaussian weights; and using the normalized Gaussian weights, performing a weighted summation of the multi-scale texture features extracted at each fixed distance value to obtain the scale-aware composite texture features, wherein the scale-aware composite texture features include composite contrast and composite homogeneity. This not only avoids computational redundancy caused by excessively high feature dimensions, but also generates robust features that are invariant to scale changes through fusion, making it easier for subsequent clustering algorithms to distinguish defects from the background in the feature space through simple homogeneity and contrast differences.

[0011] Furthermore, the multi-scale texture features extracted at each fixed distance value include: for each image patch, calculating at each preset fixed distance... The method extracts multi-scale texture features from the gray-level co-occurrence matrices in four main directions, including homogeneity and contrast features. These multi-dimensional, multi-scale texture information is then dimensionality-reduced and fused into a compact set of feature vectors. This eliminates the influence of texture orientation on the detection results, achieving rotation invariance. Regardless of the aggregate arrangement direction or crack propagation direction on the concrete surface, or angular deviation between the camera and the component, this method can completely capture texture information, avoiding missed detections due to unidirectional orientation.

[0012] Furthermore, the method for extracting homogeneity feature values ​​and contrast feature values ​​includes: calculating four contrast values ​​from the gray-level co-occurrence matrices in four main directions, and using the average of the four contrast values ​​as the contrast feature value of the image patch at a preset fixed distance; calculating four homogeneity values ​​from the four gray-level co-occurrence matrices, and using the average of the four homogeneity values ​​as the homogeneity feature value of the image patch at a preset fixed distance.

[0013] Furthermore, the K-means clustering algorithm is used to perform cluster analysis on the multiple image patches, including: using the K-Means++ algorithm to determine the initial cluster centers and setting the number of cluster centers. Multiple image patches are clustered into normal region clusters and defect region clusters.

[0014] Furthermore, after detecting surface defects in concrete components, the process also includes: performing morphological closing operations on the regions classified as defect patches to fill the holes inside the defect patches and connect adjacent defect patches. This corrects the mosaic effect and jagged edges caused by patch segmentation. By filling the tiny holes inside the defect regions and connecting adjacent discrete defect blocks, the final generated defect mask is more morphologically continuous and complete.

[0015] In a second aspect, the present invention also provides a concrete component surface defect detection system based on image segmentation, comprising a processor and a memory, wherein the memory stores a computer program, and the processor executes the computer program to implement the concrete component surface defect detection method based on image segmentation as described above.

[0016] Beneficial effects: By calculating the feature space period of each image patch through frequency domain transformation analysis, and using this as a benchmark, Gaussian weights are used to adaptively weight and fuse texture features at different distances. This method enables the feature extraction process to dynamically adapt to the physical scale of the local texture of the image, that is, it automatically focuses on small-distance analysis for fine textures and large-distance analysis for coarse defects, thereby constructing scale-aware composite texture features, which significantly improves the accuracy of identifying concrete surface defects in complex texture backgrounds. Attached Figure Description

[0017] Figure 1 This is a schematic diagram illustrating the process of detecting surface defects in concrete structures according to an embodiment of the present invention; Figure 2 This diagram schematically illustrates a comparison of the effects of prior art and the present invention based on embodiments of the present invention. Detailed Implementation

[0018] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0019] like Figure 1 and Figure 2 As shown, S101: Obtain the surface image of the concrete component and perform block processing.

[0020] To achieve high-precision detection of surface defects in concrete components, acquiring high-quality surface images is essential. Image acquisition devices are deployed on the concrete component production line, such as at the exit of the curing kiln or at component transfer stations. These cameras are positioned perpendicular to the component surface, above a high-resolution area array industrial camera. To eliminate interference from ambient light in the workshop, active, uniform strip LED light sources are placed on both sides of the camera to ensure uniform illumination of the component surface during image acquisition, avoiding localized overexposure or shadows.

[0021] To perform detailed local texture analysis, the acquired original grayscale image needs to be divided into multiple image patches. Specifically, the acquired grayscale image is divided into... indivual Image tiles of various sizes In this embodiment, the tile size... Preferred or Pixels. To avoid boundary effects in texture analysis, i.e., defects or texture features located precisely at tile boundaries and thus cut off, leading to inaccurate feature extraction, an overlap rate is set between tiles. Preferably, the overlap rate is... This overlapping setting ensures that defects or textures at the edges of tiles are fully captured by the central area of ​​at least one adjacent tile, resulting in a smoother and more continuous defect mask map.

[0022] S102: Determine the feature space period of image patches based on frequency domain analysis.

[0023] To accurately characterize the texture scale of image patches, instead of using spatial domain gradients or entropy for fuzzy estimation, physical parameters are calculated directly in the frequency domain. Specifically, a two-dimensional fast Fourier transform (2D-FFT) is performed on each image patch to obtain its complex spectrum. Subsequently, the square of the amplitude of this spectrum is calculated to obtain the two-dimensional power spectrum. .in These are frequency domain coordinates. The power spectrum reflects the distribution of energy within the image patch at different spatial frequencies.

[0024] To quantify this energy distribution, the centroid of the power spectrum, i.e., the energy-weighted average frequency, is calculated as the characteristic frequency of the patch. This is based on the fact that the energy distribution of the power spectrum is directly related to the texture scale; the energy of fine textures (such as fine aggregate) is concentrated in the high-frequency region, while the energy of coarse textures (such as honeycomb pores) is concentrated in the low-frequency region. The formula for calculating the characteristic frequency is as follows: In the formula, Indicates the first Feature frequencies of image patches Represents frequency domain coordinates, Indicates coordinates The power spectral energy value at that location, Indicates radial frequency.

[0025] It should be noted that, This only represents the average brightness (DC component) of the tiles and does not contain any texture information. Therefore, it must be excluded during the summation process to avoid affecting the accuracy of the summation. The calculation is interfered with. As can be seen from the above formula, when the block is fine aggregate, the energy... Concentrated A large area makes The value is relatively high; when the patch has a honeycomb texture, the energy... Concentrated A smaller area makes The value is low.

[0026] To guide the selection of distance parameters in the subsequent Gray-Level Co-occurrence Matrix (GLCM), the frequency indices in the frequency domain need to be converted into scale indices in the spatial domain. This involves calculating the feature spatial period that characterizes the texture scale of image tiles. The calculation formula is as follows: In the formula, Indicates the first The feature space period of an image patch, in pixels; Indicates the first Feature frequencies of each image patch; These are calibration coefficients. Used to convert frequency domain indicators Mapping to distance from the gray-level co-occurrence matrix At a comparable pixel scale. The value can be obtained by calibration using a small number of samples. As a preferred approach, in this embodiment... Values This formula reflects the inverse relationship between the characteristic space period and the characteristic frequency: fine aggregate corresponds to high... Thus, a very small value is obtained. ; while honeycomb texture corresponds to low Thus obtaining a great For example, if a certain tile calculates... Then its characteristic space period The pixel indicates that the average texture size of the tile is approximately 3 pixels.

[0027] S103: Construct scale-aware composite texture features.

[0028] To address the mismatch issue caused by extracting features from a single fixed distance, this step employs a Gaussian weighted fusion method to construct composite texture features. First, a gray-level co-occurrence matrix containing multiple fixed distance values ​​is pre-defined to calculate the distance set. The selection of this set should cover typical scales ranging from the finest mortar textures to coarse honeycomb pores. As a preferred option, this set is... .

[0029] For each image patch, at each fixed distance Calculate its gray-level co-occurrence matrix. To eliminate the influence of directionality, calculate separately... The gray-level co-occurrence matrices in four main directions are used to extract multi-scale texture features, such as contrast and homogeneity. Specifically, four contrast values ​​are calculated from the gray-level co-occurrence matrices in the four main directions, and the average of the four contrast values ​​is taken as the distance of the image patch. Contrast characteristics under Then, from the four gray-level co-occurrence matrices, four homogeneity values ​​are calculated respectively, and the average of the four homogeneity values ​​is taken as the distance of the image patch. Homogeneous eigenvalues ​​under .

[0030] Based on the characteristic space period determined in step S102 It calculates the Gaussian weights of image patches for each fixed distance value in the distance set. Its construction is based on the fact that, for the obtained feature space period... The most prominent texture feature of the tile should be determined by distance. The gray-level co-occurrence matrix contributes. The Gaussian kernel function is used to calculate each... Compared to Scale-related Gaussian weights The formula is as follows: In the formula, Indicates the first The image patch is at a distance Gaussian weights; For the first The feature space period of an image patch; It is the scale tolerance, that is, the standard deviation of the Gaussian kernel. As a hyperparameter controlling the concentration of Gaussian weights, it is preferably set to... .

[0031] This formula reflects and Match degree: when and When they are very close, the exponential part approaches 0, and the Gaussian weights... Approaching the maximum value of 1; when Much greater than or much less than When, it indicates the distance. The analysis is mismatched with the physical scale of the current tiles, and its Gaussian weights decay rapidly.

[0032] After obtaining the Gaussian weights at each distance, the Gaussian weights are first normalized to ensure that the sum of all Gaussian weights is 1. Then, the normalized Gaussian weights are used to perform weighted fusion of multi-scale texture features to construct scale-aware composite texture features. Composite contrast. and composite homogeneity The calculation formula is as follows: In the formula, Indicates the first Composite contrast of image patches. Indicates the first The image patch is at a distance Gaussian weights. Indicates the first The image patch is at a distance The contrast characteristic value under the condition. In the formula, Indicates the first Composite homogeneity of image patches. Indicates the first The image patch is at a distance Gaussian weights. Indicates the first The image patch is at a distance Homogeneous eigenvalues.

[0033] Through the above weighted fusion, the scale-aware composite texture features of each image patch are obtained. For example, the first... The scale-aware composite texture features of each image patch are This scale-aware composite texture feature can automatically adapt to the physical scale of different tiles, ensuring that feature information is no longer mismatched.

[0034] S104: Cluster Analysis and Defect Identification.

[0035] Based on the scale-aware composite texture features, a clustering algorithm is used to distinguish image patches into defective patches and normal patches. All Scale-aware composite texture features of individual image patches are stacked to form a The feature matrix is ​​then used. The K-means clustering algorithm is applied to this feature matrix.

[0036] To avoid the K-means algorithm becoming sensitive to initial centroids and getting trapped in local optima, this scheme preferentially uses the K-Means++ algorithm to intelligently select initial cluster centers. Specifically, the K-Means++ algorithm, when selecting initial centers, follows the principle that subsequently selected centers should be as far away as possible from already selected centers, using probability distributions to select initial centers, thereby significantly improving the stability and convergence speed of clustering. The number of cluster centers is set. These correspond to normal and defective areas, respectively. In the optional optimization schemes, you can also set... These correspond to the smooth mortar area, the normal aggregate area, and the honeycomb defect area, respectively, to achieve more precise separation.

[0037] After clustering is completed, analysis is performed. Defect clusters are identified by the feature values ​​of each cluster center. The specific logic is: honeycomb or pitted defect patches... Typically large, this causes Gaussian weights to concentrate over large distances. On a large scale, the contrast of the honeycomb region is extremely high and the homogeneity is extremely low. Therefore, clusters with significantly high composite contrast and significantly low composite homogeneity are marked as defective clusters; conversely, clusters with medium or low composite contrast and composite homogeneity are marked as normal clusters.

[0038] Finally, a binary mask image of the same size as the original image is generated, with all initial values ​​set to 0. If the image tiles... If a defect is clustered into a defect cluster, the corresponding pixel value in the binary mask image is set to 1. Since patch division may result in mosaic-like defect boundaries, morphological closing operations can be applied to fill the tiny holes inside the defect area and connect adjacent defect patches to form a more complete defect area, thereby achieving high-precision automatic detection of surface defects in concrete components.

[0039] The present invention also provides a surface defect detection system for concrete components based on image segmentation. The system includes a processor and a memory, the memory storing computer program instructions. When the processor executes the computer program instructions, it implements the surface defect detection method for concrete components based on image segmentation according to the first aspect of the present invention.

[0040] The system also includes other components well known to those skilled in the art, such as communication buses and communication interfaces, the settings and functions of which are known in the art and therefore will not be described in detail here.

[0041] In this invention, the aforementioned memory can be any tangible medium containing or storing a program that can be used or combined with an instruction execution system, apparatus, or device. For example, a computer-readable storage medium can be any suitable magnetic or magneto-optical storage medium, such as Resistive Random Access Memory (RRAM), Dynamic Random Access Memory (DRAM), Static Random Access Memory (SRAM), Enhanced Dynamic Random Access Memory (EDRAM), High-Bandwidth Memory (HBM), Hybrid Memory Cube (HMC), etc., or any other medium that can be used to store desired information and can be accessed by an application, module, or both. Any such computer storage medium can be part of a device or accessible to or connected to a device. Any application or module described in this invention can be implemented using computer-readable / executable instructions stored or otherwise maintained on such a computer-readable medium.

[0042] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for detecting surface defects of a concrete member based on image segmentation, characterized by, The method comprises the following steps: acquiring a surface image of a concrete member and dividing the surface image into a plurality of image patches; performing frequency domain transformation on any image patch to obtain a power spectrum, calculating a sum of products of frequencies and energy values at all non-zero frequency domain coordinates in the power spectrum, and dividing the sum by a total sum of energy values at all non-zero frequency domain coordinates to obtain a characteristic frequency of the image patch; taking a product of an inverse of the characteristic frequency and a calibration coefficient as a characteristic spatial period of the image patch; presetting a gray level co-occurrence matrix calculation distance set containing a plurality of fixed distance values, calculating a Gaussian weight of the image patch for each fixed distance value in the gray level co-occurrence matrix calculation distance set according to the characteristic spatial period; performing weighted fusion on multi-scale texture features extracted at each fixed distance value to construct a scale-aware composite texture feature of the image patch; based on the scale-aware composite texture feature, performing clustering analysis on the plurality of image patches by using a K-means clustering algorithm to distinguish defect patches and normal patches, thereby realizing detection of surface defects of the concrete member.

2. The method of claim 1, wherein the method comprises: The calculation formula of the feature space period is: ; in the formula, denotes the feature space period of the i-th image tile, is a calibration coefficient, denotes the feature frequency of the i-th image tile, denotes the feature frequency of the i-th image tile.​ 3. The method of claim 1, wherein the method comprises: The calculation formula of the characteristic frequency of the image patch is: ; In the formula, Indicates the first Feature frequencies of image patches Represents frequency domain coordinates, Indicates coordinates The power spectral energy value at that location, Indicates radial frequency.

4. The method of claim 1, wherein the method further comprises: The calculation formula of the Gaussian weight of each fixed distance value in the calculation distance set is: ; wherein represents the Gaussian weight of the th image tile at distance ; is the feature space period of the th image tile; is the scale tolerance, i.e. the standard deviation of the Gaussian kernel.

5. The method of claim 1, wherein the method further comprises: The construction of the scale-aware composite texture feature comprises: performing normalization processing on the Gaussian weight, performing weighted summation on the multi-scale texture features extracted at each fixed distance value through the normalized Gaussian weight to obtain the scale-aware composite texture feature, wherein the scale-aware composite texture feature comprises composite contrast and composite homogeneity.

6. The method of claim 5, wherein the image segmentation-based concrete member surface defect detection method is characterized by, The multi-scale texture features extracted at each fixed distance value comprise: For each image tile, at each preset fixed distance, respectively calculate Four main direction gray level co-occurrence matrixes are calculated and multi-scale texture features are extracted, wherein the multi-scale texture features include homogeneity feature values and contrast feature values.

7. The image segmentation-based concrete member surface defect detection method according to claim 6, characterized by, The extraction method of the homogeneity feature value and the contrast feature value comprises: four contrast values are respectively calculated from the gray level co-occurrence matrices in the four main directions, and an average value of the four contrast values is taken as the contrast feature value of the image patch at the preset fixed distance; four homogeneity values are respectively calculated from the four gray level co-occurrence matrices, and an average value of the four homogeneity values is taken as the homogeneity feature value of the image patch at the preset fixed distance.

8. The image segmentation-based concrete member surface defect detection method according to claim 1, characterized by, The clustering analysis on the plurality of image patches by using the K-means clustering algorithm comprises: An initial cluster center is determined using a K-Means++ algorithm, and a number of cluster centers is set The plurality of image tiles are clustered into a normal region cluster and a defect region cluster.

9. The image segmentation-based concrete member surface defect detection method according to claim 1, characterized by, After realizing the detection of the surface defects of the concrete member, the method further comprises: performing morphological closing operation on the region distinguished as the defect patch to fill holes in the defect patch and connect adjacent defect patches.

10. A concrete member surface defect detection system based on image segmentation, comprising a processor and a memory, characterized by, The memory stores a computer program, and the processor executes the computer program to realize the image segmentation-based concrete member surface defect detection method according to any one of claims 1-9.

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