Multi-Directional Structure Tensor with Log-Euclidean Patch Averaging for Robust Edge Detection
Mohamed Riadh Lajili, Zakaria Belhachmi · HAL (Le Centre pour la Communication Scientifique Directe) · 2026
In this paper, we introduce a new edge detection method based on a local directional tensor. At each pixel, we project the image gradient onto a set of evenly spaced angles and gather these projections into moments \(M_{20}, M_{02}, M_{11}\) to form a symmetric tensor \(T(x,y)\) similar to a gradient covariance matrix. To handle textured images and capture lasting directional patterns, we group these tensors into patches and compute their log-Euclidean mean, preserving the non-Euclidean geometry of the space of symmetric positive definite (SPD) matrices. By analyzing the eigenvalues of the averaged tensors and applying an adaptive threshold, our proposed method achieves precise and noise-robust edge detection. We present some numerical results of the proposed method on both natural and textured images, and compare them with those obtained using existing traditional and deep learning methods. The experiments demonstrate the efficiency and effectiveness of the proposed method