Year: 2025
Type: article
Abstract: Edge detection plays a fundamental role in image processing, as edges contain critical structural information. This paper proposes a novel edge detection model designed to simultaneously achieve robust noise suppression and precise edge localization. Within the Bayesian maximum a posteriori estimation framework, we develop a modified Mumford-Shah (MMS) variational model that incorporates image prior knowledge with probability density functions characterizing both Poisson and Gaussian noise distributions. To efficiently solve the resulting variational problem, we employ the alternating direction method of multipliers (ADMM), which decomposes the energy minimization into several tractable subproblems. We further provide theoretical analysis demonstrating the algorithm's convergence under specific conditions. Extensive numerical experiments across varying levels of mixed noise contamination demonstrate that our method significantly outperforms classical edge detection approaches in both efficiency and accuracy.
Source: Inverse Problems and Imaging
DOI: 10.3934/ipi.2025048
Authors: Yuying Shi, Zhihan Zeng, Jingjing Liu, Wei Wan
Institution: North China Electric Power University
Language: English
Subfield: Computer Vision and Pattern Recognition
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Awards: G1951465523, G7376023051
OpenAlex ID: W7083492793