Detection of Pits by Conjugate Lines: An Algorithm for Segmentation of Overlapping and Adhesion Targets in DE-XRT Sorting Images of Coal and Gangue  
[PERSON]  
School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China  
1  
[PERSON]  
Correspondence: [EMAIL_ADDRESS] School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China  
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Yongcun Guo  
School of Mechanical Engineering, Anhui University of Science and Technology, Huainan 232001, China  
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Footnote 2: email: {heihe,hang,wong,j  
model to extract the image features of coal dust particles and segment the conglutinated particles by up-sampling on un-pooling. This method requires many learning samples in the early stage and takes much time. Compared with the WA, the pit detection and matching algorithm are more controllable. The segmentation of adhesion targets can be well completed by improving the accuracy of pits through algorithm design and combining with the principle of matching pits [24]. However, the pit detection accuracy and matching principle are difficult to meet the requirements of multi-scale, multi-target, and multi-adhesion segmentation of coal and gangue images. [PERSON] et al. [25] and [PERSON] et al. [26] adopted a chain code coding algorithm to calculate the change in the edge curvature of the adhesion target and set the curvature threshold to select the pit. [PERSON] et al. [11] and [PERSON] et al. [27] segmented overlapping targets by obtaining concave defects [28] of overlapping targets and then connecting the minimum distance between concave defects. [PERSON] et al. [29], [PERSON] et al. [30], and [PERSON] et al. [13] traversed the non-zero-pixel area of the peripheral square area (\(n\times n\)) or circular area (\(r=l\)) of the binary edge pixels of the adhesion target. They set the area threshold to select the pit. By calculating and judging the included angle between the binary edge pixels of the adhesion target and its front point and back point, [PERSON] [31] set the angle threshold to select the pit. Because there are different degrees of concave areas in the circumferential direction of irregular-shaped coal and gangue, the above method uses a simple threshold to filter and select pit points. Eventually, the number of pits detected is inaccurate. [PERSON] et al. [32] used a single straight line to detect pits. This pit detection method is still subject to the influence of the adhesion form; for example, in the case where a single concave defect has multiple pits, a straight line will not detect all of the pits. In the prior art, the detection rate of pits is low. Affected by the irregular shape of coal and gangue, the compatibility decreases. Generally, too many or too few pits are detected. For this reason, to solve the problem of segmentation and location of overlapping images of coal and gangue with multi-scale, multi-objective, and various adhesion forms, this paper proposes an algorithm for detecting pit points and segmenting images by conjugate lines. Moreover, the adhesion forms are divided into closed-loop and open-loop adhesions (CLA and OLA), and the discrimination method of adhesion forms is provided. Furthermore, concave defects are divided into concave defects at convex hull edge and concave defects at non-convex hull edge, while open- and closed-loop pit detection algorithms are designed. This algorithm judges the pit with the set constraint by detecting the position relationship and distance of the pixel point relative to conjugate lines. It can accurately detect all pits. Finally, the minimum distance search method is adopted to acquire the dividing line corresponding to the pits to complete the image segmentation. The primary objectives and contributions of this paper are as follows:  
1. This paper defines the adhesion form of the coal and gangue image target and provides the judgment method. Concave defects are classified according to different adhesion forms, and a pit point detection algorithm is designed for the concave defects. 2.