A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment
Abstract
This paper is devoted to the mathematical analysis of a system of pseudo-parabolic partial differential equations governed by an energy functional, associated with anisotropic monochrome image processing. The energy functional is based on the one proposed by [Berkels et al. Cartoon extraction based on anisotropic image classification, SFB 611, 2006], which incorporates an orientation auto-adjustment mechanism, and our energy is a simplified version which reduces the order of derivatives to improve computational efficiency. The aim of this paper is to establish a stable minimization process that addresses some instability of the algorithm caused by the reduction of derivative order. As a part of the study, we here prove Main Theorems concerned with the well-posedness of the pseudo-parabolic system, and provide a mathematically rigorous guarantee for the stability of the image denoising process derived from our system.
Cite
@article{arxiv.2408.12847,
title = {A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment},
author = {Harbir Antil and Daiki Mizuno and Ken Shirakawa and Naotaka Ukai},
journal= {arXiv preprint arXiv:2408.12847},
year = {2024}
}
Comments
28 pages