The topological gradient method for semi-linear problems and application to edge detection and noise removal

Audric  Drogoul; Gilles  Aubert

doi:10.3934/ipi.2016.10.51

Article Contents

2016, Volume 10, Issue 1: 51-86. Doi: 10.3934/ipi.2016.10.51

This issue Previous Article A fractional-order derivative based variational framework for image denoising Next Article Common midpoint versus common offset acquisition geometry in seismic imaging

The topological gradient method for semi-linear problems and application to edge detection and noise removal

Audric Drogoul^1, and
Gilles Aubert^1,

1.
Univ. Nice Sophia Antipolis, CNRS, LJAD, UMR 7351, 06100 Nice

Received: November 30, 2014

Revised: June 30, 2015

Published: January 2016

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Abstract

The goal of this paper is to apply the topological gradient method to edge detection and noise removal for images degraded by various noises and blurs. First applied to edge detection for images degraded by a Gaussian noise, we propose here to extend the method to blurred images contaminated either by a multiplicative noise of gamma law or to blurred Poissonian images. We compute, both for perforated and cracked domains, the topological gradient for each noise model. Then we present an edge detection/restoration algorithm based on this notion and we apply it to the two degradation models previously described. We compare our method with other classical variational approaches such that the Mumford-Shah and TV restoration models and with the classical Canny edge detector. Some experimental results showing the efficiency, the robustness and the rapidity of the method are presented.

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Mathematics Subject Classification: 35J91, 49Q10, 49Q12, 94A08, 94A13.

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