A Variational based Model for Edge Detection Using Local Meshless Method

Abstract

This article presents the Local Meshless Method (LMM) for numerically solving Partial Differential Equations (PDEs) conncected with a Total Variation (TV) regularization-based edge detection model. The suggested meshless method not only restores images but also effectively preserves edges. This advantage arises from its independence from mesh generation, allowing it to handle complex geometries, significant irregularities, and discontinuities. Experimental results show that the proposed meshless method achieves excellent results in terms of image denoising, specifically measured by Signal to Noise Ratio (SNR), and edge detection, evaluated using the Edge Preservation Index (EPI), when compared to traditional mesh-based methods.