Visual reconstruction
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
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Deterministic edge-preserving regularization in computed imaging
IEEE Transactions on Image Processing
Variational approach for edge-preserving regularization using coupled PDEs
IEEE Transactions on Image Processing
Roof-edge preserving image smoothing based on MRFs
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Image segmentation and selective smoothing by using Mumford-Shah model
IEEE Transactions on Image Processing
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In this paper, the Mumford-Shah (MS) model and its variations are studied for image segmentation. It is found that using the piecewise constant approximation, we cannot detect edges with low contrast. Therefore other terms, such as gradient and Laplacian, are included in the models. To simplify the problem, the gradient of the original image is used in the Rudin-Osher-Fatemi (ROF) like model. It is found that this approximation is better than the piecewise constant approximation for some images since it can detect the low contrast edges of objects. Linear approximation is also used for both MS and ROF like models. It is found that the linear approximation results are comparable with the results of the models using gradient and Laplacian terms.