Edge Detection of Square Wave Stripe Images for Three-Dimensional Measurement of Granular Matter

Abstract

To address the challenges of edge detection in square-wave fringe images corrupted by discrete spot noise during granular kinematics measurement, this paper proposes an edge detection framework based on gradient magnitude thresholding and applies it to the 3D reconstruction of granular beds. First, a multi-scale Perona-Malik anisotropic diffusion model is employed for denoising; by constructing an image pyramid and adaptively adjusting diffusion coefficients across scales, the method effectively suppresses spot noise while preserving fringe integrity. Second, the Otsu algorithm is utilized for automated threshold segmentation, where morphological structuring elements are adaptively refined according to fringe curvature. Finally, to circumvent the limitations of the traditional Canny algorithm—specifically edge fragmentation and hysteresis tracking failure—a gradient magnitude thresholding-based extraction method is selected. Numerical simulations on images with a curvature of 0.01 and 2000 noise points demonstrate that the proposed pipeline significantly outperforms direct Canny detection, increasing the Intersection over Union (IoU) from 0.51 to 0.71 and the F1-score from 0.67 to 0.82. Experimental validation on static granular beds yields a planar reconstruction error within one particle diameter (0.8 - 1.0 mm) and a slope error of 0.0015. By leveraging the structural priors of square-wave fringes, this method provides a reliable technical foundation for three-dimensional measurements in the field of particle kinematics.