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Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time
In this paper, we introduce a new method for image smoothing based on a fourth-order PDE model. The method is tested on a broad range of real medical magnetic resonance images, both in space andExpand
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Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models
In image processing, the Rudin-Osher-Fatemi (ROF) model [L. Rudin, S. Osher, and E. Fatemi, Phys. D, 60 (1992), pp. 259-268] based on total variation (TV) minimization has proven to be very useful.Expand
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A study on continuous max-flow and min-cut approaches
We propose and study novel max-flow models in the continuous setting, which directly map the discrete graph-based max-flow problem to its continuous optimization formulation. We show such aExpand
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A Continuous Max-Flow Approach to Potts Model
We address the continuous problem of assigning multiple (unordered) labels with the minimum perimeter. The corresponding discrete Potts model is typically addressed with a-expansion which canExpand
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A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
Minimization of functionals related to Euler's elastica energy has a wide range of applications in computer vision and image processing. A high order nonlinear partial differential equation (PDE)Expand
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A variant of the level set method and applications to image segmentation
In this paper we propose a variant of the level set formulation for identifying curves separating regions into different phases. In classical level set approaches, the sign of n level set functionsExpand
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A binary level set model and some applications to Mumford-Shah image segmentation
In this paper, we propose a PDE-based level set method. Traditionally, interfaces are represented by the zero level set of continuous level set functions. Instead, we let the interfaces beExpand
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Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
A noise removal technique using partial differential equations (PDEs) is proposed here. It combines the Total Variational (TV) filter with a fourth-order PDE filter. The combined technique is able toExpand
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Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach
This paper is devoted to the optimization problem of continuous multi-partitioning, or multi-labeling, which is based on a convex relaxation of the continuous Potts model. In contrast to previousExpand
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A Robust Finite Element Method for Darcy-Stokes Flow
Finite element methods for a family of systems of singular perturbation problems of a saddle point structure are discussed. The system is approximately a linear Stokes problem when the perturbationExpand
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