Visual reconstruction
Weakly differentiable functions
Weakly differentiable functions
Parallel and deterministic algorithms from MRFs: surface reconstruction and integration
ECCV 90 Proceedings of the first european conference on Computer vision
A common framework for image segmentation
International Journal of Computer Vision
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
Recognizing corners by fitting parametric models
International Journal of Computer Vision
A multiscale algorithm for image segmentation by variational method
SIAM Journal on Numerical Analysis
Variational methods in image segmentation
Variational methods in image segmentation
Markov random field modeling in computer vision
Markov random field modeling in computer vision
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Local Versus Nonlocal Computation of Length of Digitized Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Framework for Low Level Feature Extraction
ECCV '94 Proceedings of the Third European Conference-Volume II on Computer Vision - Volume II
A Variational Approach to the Design of Early Vision Algorithms
Proceedings of the 7th TFCV on Theoretical Foundations of Computer Vision
Isophotes Selection and Reaction-Diffusion Model for Object Boundaries Estimation
International Journal of Computer Vision
Optimal Level Curves and Global Minimizers of Cost Functionals in Image Segmentation
Journal of Mathematical Imaging and Vision
Level Lines as Global Minimizers of Energy Functionals in Image Segmentation
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Image Labeling and Grouping by Minimizing Linear Functionals over Cones
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
An Adaptive Finite Element Method for Large Scale Image Processing
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Splines in Higher Order TV Regularization
International Journal of Computer Vision
Diffusion-Like reconstruction schemes from linear data models
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
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We analyze a variational approach to image segmentation that isbased on a strictly convex non-quadratic cost functional.The smoothness term combines a standard first-ordermeasure for image regions with a total-variation basedmeasure for signal transitions. Accordingly, the costs associatedwith “discontinuities” are givenby the length of level lines and local image contrast.For real images, this provides a reasonable approximation of thevariational model of Mumford and Shah that has been suggested asa generic approach to image segmentation.The global properties of the convex variational model are favorableto applications: Uniqueness of the solution, continuous dependenceof the solution on both data and parameters, consistent and efficientnumerical approximation of the solution with the FEM-method.Various global and local properties of the convex variational modelare analyzed and illustrated with numerical examples. Apart fromthe favorable global properties, the approach is shown to providea sound mathematical model of a useful locally adaptive smoothingprocess. A comparison is carried out with results of a region-growing technique related to the Mumford-Shah model.