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Mumford-Shah and Potts functionals are powerful variational models for regularization which are widely used in signal and image processing; typical applications are edge-preserving denoising and segmentation. Being both non-smooth and…

Numerical Analysis · Mathematics 2016-02-11 Andreas Weinmann , Laurent Demaret , Martin Storath

This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…

Numerical Analysis · Mathematics 2025-08-29 Zhenyu Zhao , Yanfei Wang

In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte-Carlo or other…

Optimization and Control · Mathematics 2007-05-23 Jianhong Shen

Given values of a piecewise smooth function $f$ on a square grid within a domain $\Omega$, we look for a piecewise adaptive approximation to $f$. Standard approximation techniques achieve reduced approximation orders near the boundary of…

Numerical Analysis · Mathematics 2020-12-04 Sergio Amat , David Levin , Juan Ruiz-Álvarez

Many segmentation tasks for biomedical images can be modeled as the minimization of an energy function and solved by a class of max-flow and min-cut optimization algorithms. However, the segmentation accuracy is sensitive to the contrasting…

Computer Vision and Pattern Recognition · Computer Science 2021-09-03 Yan Shen , Zhanghexuan Ji , Mingchen Gao

In the paper the optimal image segmentation by means of piecewise constant approximations is considered. The optimality is defined by a minimum value of the total squared error or by equivalent value of standard deviation of the…

Computer Vision and Pattern Recognition · Computer Science 2012-10-09 M. Kharinov

We analyze a finite-difference approximation of a functional of Ambrosio-Tortorelli type in brittle fracture, in the discrete-to-continuum limit. In a suitable regime between the competing scales, namely if the discretization step $\delta$…

Analysis of PDEs · Mathematics 2020-07-31 Vito Crismale , Giovanni Scilla , Francesco Solombrino

We consider a family $\{(u_\varepsilon, v_\varepsilon)\}_{\varepsilon>0}$ of critical points of the Ambrosio-Tortorelli functional. Assuming a uniform energy bound, the sequence $\{(u_\varepsilon, v_\varepsilon)\}_{\varepsilon>0}$ converges…

Analysis of PDEs · Mathematics 2026-01-19 Jean-François Babadjian , Martin Rakovsky , Rémy Rodiac

The main objective of image segmentation is to divide an image into homogeneous regions for further analysis. This is a significant and crucial task in many applications such as medical imaging. Deep learning (DL) methods have been proposed…

Image and Video Processing · Electrical Eng. & Systems 2023-06-27 Junying Meng , Weihong Guo , Jun Liu , Mingrui Yang

In this paper, we propose a novel retinal layer boundary model for segmentation of optical coherence tomography (OCT) images. The retinal layer boundary model consists of 9 open parametric contours representing the 9 retinal layers in OCT…

Computer Vision and Pattern Recognition · Computer Science 2018-08-10 Jinming Duan , Weicheng Xie , Ryan Wen Liu , Christopher Tench , Irene Gottlob , Frank Proudlock , Li Bai

The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…

Functional Analysis · Mathematics 2007-05-23 Angela Kempe , Volkmar Liebscher , Gerhard Winkler , Olaf Wittich

This work focuses on a parameter-free joint piecewise smooth image denoising and contour detection. Formulated as the minimization of a discrete Mumford-Shah functional and estimated via a theoretically grounded alternating minimization…

Image and Video Processing · Electrical Eng. & Systems 2023-02-01 Charles-Gérard Lucas , Barbara Pascal , Nelly Pustelnik , Patrice Abry

Image segmentation is an important component of many image understanding systems. It aims to group pixels in a spatially and perceptually coherent manner. Typically, these algorithms have a collection of parameters that control the degree…

Computer Vision and Pattern Recognition · Computer Science 2018-02-02 Marc Bosch , Christopher M. Gifford , Austin G. Dress , Clare W. Lau , Jeffrey G. Skibo , Gordon A. Christie

We propose a software platform that integrates methods and tools for multi-objective parameter auto- tuning in tissue image segmentation workflows. The goal of our work is to provide an approach for improving the accuracy of nucleus/cell…

Distributed, Parallel, and Cluster Computing · Computer Science 2018-10-09 Luis F. R. Taveira , Tahsin Kurc , Alba C. M. A. Melo , Jun Kong , Erich Bremer , Joel H. Saltz , George Teodoro

We transpose an optimal control technique to the image segmentation problem. The idea is to consider image segmentation as a parameter estimation problem. The parameter to estimate is the color of the pixels of the image. We use the…

Numerical Analysis · Mathematics 2011-05-24 Hend Ben Ameur , Guy Chavent , Francois Clément , Pierre Weis

In this paper, we introduce a novel approach for active contours with free endpoints. A scheme is presented for image segmentation and restoration based on a discrete version of the Mumford-Shah functional where the contours can be both…

Computer Vision and Pattern Recognition · Computer Science 2016-04-20 Heike Benninghoff , Harald Garcke

Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we…

Computer Vision and Pattern Recognition · Computer Science 2024-06-05 Elisha Dayag , Kevin Bui , Fredrick Park , Jack Xin

Semantic image segmentation is an important computer vision task that is difficult because it consists of both recognition and segmentation. The task is often cast as a structured output problem on an exponentially large output-space, which…

Computer Vision and Pattern Recognition · Computer Science 2017-09-07 Payman Yadollahpour

The Mumford-Shah (MS) model is an important technique for mesh segmentation. Many existing researches focus on piecewise constant MS mesh segmentation model with total variation regularization, which pursue the shortest length of…

Computational Geometry · Computer Science 2025-07-28 Huayan Zhang , Shanqiang Wang , Xiaochao Wang

Segmentation is the process of partitioning a digital image into multiple segments (sets of pixels). Such common segmentation tasks including segmenting written text or segmenting tumors from healthy brain tissue in an MRI image, etc.…

Computer Vision and Pattern Recognition · Computer Science 2011-07-18 Rami Cohen