Manually mapping fractures in construction stone mines is challenging, time-consuming, and hazardous. In this method, there is no physical access to all points. In contrast, digital image processing offers a safe, cost-effective, and fast alternative, with the capability to map all joints. In this study, two methods of detecting the trace of discontinuities using image processing in construction stone mines are presented. To achieve this, we employ two modified Hough transform algorithms and the degree of neighborhood technique. Initially, we introduced a method for selecting the best edge detector and smoothing algorithms. Subsequently, the Canny detector and median smoother were identified as the most efficient tools. To trace discontinuities using the mentioned methods, common preprocessing steps were initially applied to the image. Following this, each of the two algorithms followed a distinct approach. The Hough transform algorithm was first applied to the image, and the traces were represented through line drawings. Subsequently, the Hough transform results were refined using fuzzy clustering and reduced clustering algorithms, along with a novel algorithm known as the farthest points' algorithm. Additionally, we developed another algorithm, the degree of neighborhood, tailored for detecting discontinuity traces in construction stones. After completing the common preprocessing steps, the thinning operation was performed on the target image, and the degree of neighborhood for lineament pixels was determined. Subsequently, short lines were removed, and the discontinuities were determined based on the degree of neighborhood. In the final step, we connected lines that were previously separated using the method to be described. The comparison of results demonstrates that image processing is a suitable tool for identifying rock mass discontinuity traces. Finally, a comparison of two images from different construction stone mines presented at the end of this study reveals that in images with fewer traces of discontinuities and a softer texture, both algorithms effectively detect the discontinuity traces.