## 1 Introduction  
A belt conveyor is a friction transmission-based machine that transports materials in a continuous manner. It is the preferred equipment for the continuous conveying of bulk materials and is widely used in mines, ports, and whaves; for cement; and in agriculture, the chemical industry, and other fields [1]. In recent years, under the demands of Industry 4.0 [2, 3] and \"energy conservation and emission reduction\" [4], belt conveyors have been developed for use over long distances, at high belt speeds, on a large scale, in intelligence [5, 6], and in ways that save energy [7, 8]. The research and development of reliable equipment and technology that efficiently monitors operating conditions have gradually become an important component to ensure the reliable operation of belt conveyors. Belt deviation, as one of the most common operating failures of belt conveyors, is closely related to the processing quality and installation accuracy of idlers and rollers, the balance of material loading, and the quality of conveyor belt joints [9, 10]. Deviation will lead to the abnormal wear of the belt edge, which may cause problems such as material spillage and the increased energy consumption of the conveyor [11]. Serious deviation will directly lead to tearing accidents [12], trigger safety accidents, and affect the normal production of enterprises [13]. Therefore, it is of great practical significance to effectively monitor the belt deviation state. Currently, most of the applied deviation monitoring methods rely on a deviation sensor [13]. Essentially, this is a multi-stage travel switch that outputs a switch signal. In recent years, non-contact measurement methods based on machine vision have also been designed. Specific implementation methods include the traditional image-processing-based straight-line detection method, deep learning-based deviation state classification, target segmentation-based conveyor belt region positioning, and the decision method based on idler number identification and comparison. The traditional image-processing-based straight-line detection method is mainly represented by Canny edge detection and Hough line detection [14; 15; 16]. However, it requires a complex image processing procedure due to the influence of the complex working environment and conveying material flow in practical applications, including the acquisition of the region of interest, grayscale transformation, edge detection, connected domain analysis, morphological processing, Hough line detection, etc. [15]. During this period, a large number of threshold determinations are involved, and the overall practicability is poor, especially when the camera is tilted: the larger the field of view, the more complex the processing operations required to avoid the interference of other targets. Then, the classification of the deviation state based on deep learning [17] and the judgment method based on the identification of the number of idlers beside the belt can only be used to realize the qualitative measurement of the deviation state of the belt. This cannot meet the needs of quantitative measurement and is not conducive to determining the deviation rules. The location of the conveyor belt area based on target segmentation [18; 19] can easily separate the conveyor belt area from the background of the field of view, but target segmentation is a pixel-level operation. It is difficult to create a dataset in the pre-production stage, and it is also difficult to achieve quantitative measurement. In comparison, it is more feasible to obtain the belt edge line directly through the segmentation method, but if the judgment of the deviation state is to be realized, it is also necessary to further fit the obtained segmentation results. In view of the above problems, considering the straight-line feature of the belt edge, in this work, we propose a quantitative monitoring method for the deviation state of the conveyor belt based on the intrinsic features of the prediction box.