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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.…

In this paper we study a variant to Chan-Vese image segmentation model with rectilinear anisotropy. We show existence of minimizers in the $2$-phases case and how they are related to the (anisotropic) Rudin-Osher-Fatemi denoising model…

We propose an unsupervised image segmentation approach, that combines a variational energy functional and deep convolutional neural networks. The variational part is based on a recent multichannel multiphase Chan-Vese model, which is…

This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. We first integrate the Allen--Cahn term and the Chan--Vese fitting energy term to establish an energy functional, whose minimum locates the…

We consider an image decomposition model involving a variational (minimization) problem and an evolutionary partial differential equation (PDE). We utilize a linear inhomogenuous diffusion constrained and weighted total variation (TV)…

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…

Image segmentation is an important task in the domain of computer vision and medical imaging. In natural and medical images, intensity inhomogeneity, i.e. the varying image intensity, occurs often and it poses considerable challenges for…

This paper addresses streak reduction in limited angle tomography. Although the iterative reweighted total variation (wTV) algorithm reduces small streaks well, it is rather inept at eliminating large ones since total variation (TV)…

Intensity inhomogeneities in images constitute a considerable challenge in image segmentation. In this paper we propose a novel biconvex variational model to tackle this task. We combine a total variation approach for multi class…

We present a new vectorial total variation method that addresses the problem of color consistent image filtering. Our approach is inspired from the double-opponent cell representation in the human visual cortex. Existing methods of…

This paper considers the constrained total variation (TV) denoising problem for complex-valued images. We extend the definition of TV seminorms for real-valued images to dealing with complex-valued ones. In particular, we introduce two…

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…

In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…

Image segmentation is a fundamental and challenging task in image processing and computer vision. The color image segmentation is attracting more attention due to the color image provides more information than the gray image. In this paper,…

Image segmentation is the foundation of several computer vision tasks, where pixel-wise knowledge is a prerequisite for achieving the desired target. Deep learning has shown promising performance in supervised image segmentation. However,…

The total variation (TV) method is an image denoising technique that aims to reduce noise by minimizing the total variation of the image, which measures the variation in pixel intensities. The TV method has been widely applied in image…

In this paper, we present a comprehensive study and analysis of the Chan-Vese algorithm for image segmentation. We employ a discretized scheme derived from the empirical study of the Chan-Vese model's functional energy and its partial…

Total variation (TV) is a powerful regularization method that has been widely applied in different imaging applications, but is difficult to apply to diffuse optical tomography (DOT) image reconstruction (inverse problem) due to complex and…

Selective segmentation involves incorporating user input to partition an image into foreground and background, by discriminating between objects of a similar type. Typically, such methods involve introducing additional constraints to…

The Chan-Vese (CV) model is a classic region-based method in image segmentation. However, its piecewise constant assumption does not always hold for practical applications. Many improvements have been proposed but the issue is still far…