# A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment

Source: [A gradient system based on anisotropic monochrome image processing with orientation auto-adjustment](<https://www.sota2.com/research/paper/68fa5c591e209131ce9d017e>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:34:29.829Z

Authors: Harbir Antil, Daiki Mizuno, Ken Shirakawa, Naotaka Ukai

Published: 2024-08-23T05:32:53.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2408.12847>)

[PDF](<https://arxiv.org/pdf/2408.12847.pdf>)