相关论文: Colour image segmentation by the vector-valued All…

The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…

Image Segmentation is a technique of partitioning the original image into some distinct classes. Many possible solutions may be available for segmenting an image into a certain number of classes, each one having different quality of…

We propose a path cover adaptive algebraic multigrid (PC-$\alpha$AMG) method for solving linear systems of weighted graph Laplacians and can also be applied to discretized second order elliptic partial differential equations. The…

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…

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…

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical…

Recent state-of-the-art image segmentation algorithms are mostly based on deep neural networks, thanks to their high performance and fast computation time. However, these methods are usually trained in a supervised manner, which requires…

Segmentation remains an important problem in image processing. For homogeneous (piecewise smooth) images, a number of important models have been developed and refined over the past several decades. However, these models often fail when…

We consider the inverse problem of recovering a binary function from blurred and noisy data. Such problems arise in many applications, for example image processing and optimal control of PDEs. Our formulation is based on the Mumford-Shah…

Practical image segmentation tasks concern images which must be reconstructed from noisy, distorted, and/or incomplete observations. A recent approach for solving such tasks is to perform this reconstruction jointly with the segmentation,…

This paper demonstrates the impact of a phase field method on shape registration to align shapes of possibly different topology. It yields new insights into the building of discrepancy measures between shapes regardless of topology, which…

As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic…

To address the challenge of segmenting noisy images with blurred or fragmented boundaries, this paper presents a robust version of Variational Model Based Tailored UNet (VM_TUNet), a hybrid framework that integrates variational methods with…

Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type equations, have been widely used to investigate interfacial dynamic problems. Designing accurate, efficient, and stable numerical algorithms for solving the phase…

In this paper, we describe an implementation of the two-phase image segmentation algorithm proposed by Goldstein, Bresson, Osher in \cite{gold:bre}. This algorithm partitions the domain of a given 2d image into foreground and background…

We propose, analyze and realize a variational multiclass segmentation scheme that partitions a given image into multiple regions exhibiting specific properties. Our method determines multiple functions that encode the segmentation regions…

We address the problem of soft color segmentation, defined as decomposing a given image into several RGBA layers, each containing only homogeneous color regions. The resulting layers from decomposition pave the way for applications that…

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…

Image segmentation is the problem of partitioning an image into different subsets, where each subset may have a different characterization in terms of color, intensity, texture, and/or other features. Segmentation is a fundamental component…

In this paper we propose an algorithm for the detection of edges in images that is based on topological asymptotic analysis. Motivated from the Mumford--Shah functional, we consider a variational functional that penalizes oscillations…