Segmentation in Measure Spaces

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2024-04-20 DOI:10.1007/s00245-024-10134-5

Salvador Moll, Vicent Pallardó-Julià, Marcos Solera

引用次数: 0

Abstract

We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most well-studied variational models in image processing: the Rudin–Osher–Fatemi model for image denoising (ROF) and the Mumford–Shah model for image segmentation (MS). We show the linkage between the ROF model and the two phases piecewise constant case of MS in perimeter measure spaces. We show applications of our results to nonlocal image segmentation, via discrete weighted graphs, and to multiclass classification on high dimensional spaces.

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度量空间中的分段

我们将周长度量空间的抽象概念视为一个非常通用的框架，在这个框架中，我们可以正确地考虑图像处理中研究最深入的两个变分模型：用于图像去噪的 Rudin-Osher-Fatemi 模型（ROF）和用于图像分割的 Mumford-Shah 模型（MS）。我们展示了 ROF 模型与周长度量空间中 MS 的两相片断常数情况之间的联系。我们展示了我们的成果在非局部图像分割（通过离散加权图）和高维空间多类分类中的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.