Denoising algorithm of the modified Gray-Scott model on non-uniform grids

IF 2.5 2区数学 Q1 MATHEMATICS, APPLIED

Computers & Mathematics with Applications Pub Date : 2025-07-23 DOI:10.1016/j.camwa.2025.07.016

Shanshan Ge , Jian Wang

{"title":"Denoising algorithm of the modified Gray-Scott model on non-uniform grids","authors":"Shanshan Ge , Jian Wang","doi":"10.1016/j.camwa.2025.07.016","DOIUrl":null,"url":null,"abstract":"<div><div>This paper introduces an denoising algorithm based on the Gray-Scott (GS) model, which adopts non-uniform grids and highly adaptive numerical strategy to achieve effective denoising for two-dimensional (2D) and three-dimensional (3D) models. This method adjusts the grid density based on regional characteristics: dense grids are used in the area of interest to improve local accuracy, and sparse grids are used in non-critical areas to enhance the overall computational efficiency. In order to enhance the robustness and shape preserving ability, we modify the original GS model by replacing <span><math><mo>(</mo><mi>F</mi><mo>+</mo><mi>k</mi><mo>)</mo><mi>v</mi></math></span> with <span><math><mo>(</mo><mi>F</mi><mo>+</mo><mi>k</mi><mo>)</mo><mo>(</mo><mi>v</mi><mo>−</mo><msub><mrow><mi>v</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></math></span>, which effectively relives the volume shrinkage and shape distortion problems, and achieves the retention of structural details and effective suppression of noise. Numerical experiments show that our algorithm can maintain key geometric features while improving the smoothness, and has excellent denoising performance and extensive applicability.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"195 ","pages":"Pages 191-211"},"PeriodicalIF":2.5000,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers & Mathematics with Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0898122125003074","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

Abstract

This paper introduces an denoising algorithm based on the Gray-Scott (GS) model, which adopts non-uniform grids and highly adaptive numerical strategy to achieve effective denoising for two-dimensional (2D) and three-dimensional (3D) models. This method adjusts the grid density based on regional characteristics: dense grids are used in the area of interest to improve local accuracy, and sparse grids are used in non-critical areas to enhance the overall computational efficiency. In order to enhance the robustness and shape preserving ability, we modify the original GS model by replacing

(F + k) v

with

(F + k) (v - v_{0})

, which effectively relives the volume shrinkage and shape distortion problems, and achieves the retention of structural details and effective suppression of noise. Numerical experiments show that our algorithm can maintain key geometric features while improving the smoothness, and has excellent denoising performance and extensive applicability.

查看原文本刊更多论文

改进Gray-Scott模型在非均匀网格上的去噪算法

本文介绍了一种基于Gray-Scott （GS）模型的去噪算法，该算法采用非均匀网格和高自适应数值策略对二维（2D）和三维（3D）模型进行有效去噪。该方法根据区域特征调整网格密度，在感兴趣区域使用密集网格来提高局部精度，在非关键区域使用稀疏网格来提高整体计算效率。为了增强鲁棒性和形状保持能力，我们将原GS模型的（F+k）v替换为（F+k）（v−v0），有效地解决了体积收缩和形状畸变问题，实现了结构细节的保留和对噪声的有效抑制。数值实验表明，该算法在保持关键几何特征的同时提高了平滑度，具有良好的去噪性能和广泛的适用性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Computers & Mathematics with Applications 工程技术-计算机：跨学科应用

CiteScore

5.10

自引率

10.30%

发文量

396

审稿时长

9.9 weeks

期刊介绍： Computers & Mathematics with Applications provides a medium of exchange for those engaged in fields contributing to building successful simulations for science and engineering using Partial Differential Equations (PDEs).