Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Inexact and preconditioned Uzawa algorithms for saddle point problems
SIAM Journal on Numerical Analysis - Special issue: the articles in this issue are dedicated to Seymour V. Parter
International Journal of Computer Vision
Statistical Region Snake-Based Segmentation Adapted to Different Physical Noise Models
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
Semi-Implicit Level Set Methods for Curvature and Surface Diffusion Motion
Journal of Scientific Computing
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Influence of the Noise Model on Level Set Active Contour Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Level Set Evolution without Re-Initialization: A New Variational Formulation
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
Speckle-Constrained Filtering of Ultrasound Images
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
International Journal of Computer Vision
A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
Journal of Mathematical Imaging and Vision
Bivariate density estimation using BV regularisation
Computational Statistics & Data Analysis
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Restoration of astrophysical images: the case of poisson data with additive Gaussian noise
EURASIP Journal on Applied Signal Processing
Lagrange Multiplier Approach to Variational Problems and Applications
Lagrange Multiplier Approach to Variational Problems and Applications
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
Total Variation Processing of Images with Poisson Statistics
CAIP '09 Proceedings of the 13th International Conference on Computer Analysis of Images and Patterns
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Geometric Applications of the Split Bregman Method: Segmentation and Surface Reconstruction
Journal of Scientific Computing
Convex relaxation for multilabel problems with product label spaces
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
A Variational Model to Remove the Multiplicative Noise in Ultrasound Images
Journal of Mathematical Imaging and Vision
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
Optimality bounds for a variational relaxation of the image partitioning problem
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
Energy minimization based segmentation and denoising using a multilayer level set approach
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
IEEE Transactions on Image Processing
Level Set Segmentation With Multiple Regions
IEEE Transactions on Image Processing
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Image segmentation is one of the fundamental problems in computer vision and image processing. In the recent years mathematical models based on partial differential equations and variational methods have led to superior results in many applications, e.g., medical imaging. A majority of works on image segmentation implicitly assume the given image to be biased by additive Gaussian noise, for instance the popular Mumford-Shah model. Since this assumption is not suitable for a variety of problems, we propose a region-based variational segmentation framework to segment also images with non-Gaussian noise models. Motivated by applications in biomedical imaging, we discuss the cases of Poisson and multiplicative speckle noise intensively. Analytical results such as the existence of a solution are verified and we investigate the use of different regularization functionals to provide a-priori information regarding the expected solution. The performance of the proposed framework is illustrated by experimental results on synthetic and real data.