Visual reconstruction
Fast Algorithms for Low-Level Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Variational methods in image segmentation
Variational methods in image segmentation
Region Competition: Unifying Snakes, Region Growing, and Bayes/MDL for Multiband Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Regularization, Scale-Space, and Edge Detection Filters
Journal of Mathematical Imaging and Vision
Fast Approximate Energy Minimization via Graph Cuts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Diffusion Snakes: Introducing Statistical Shape Knowledge into the Mumford-Shah Functional
International Journal of Computer Vision
A Variational Framework for Active and Adaptative Segmentation of Vector Valued Images
MOTION '02 Proceedings of the Workshop on Motion and Video Computing
Natural Image Statistics for Natural Image Segmentation
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
On the statistical interpretation of the piecewise smooth Mumford-Shah functional
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Efficient segmentation of piecewise smooth images
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Three-dimensional shape knowledge for joint image segmentation and pose estimation
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
International Journal of Computer Vision
The piecewise smooth Mumford-Shah functional on an arbitrary graph
IEEE Transactions on Image Processing
Radial basis function based level set interpolation and evolution for deformable modelling
Image and Vision Computing
Learning a nonlinear distance metric for supervised region-merging image segmentation
Computer Vision and Image Understanding
Multichannel segmentation using contour relaxation: fast super-pixels and temporal propagation
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Texture segmentation using vector-valued Chan-Vese model driven by local histogram
Computers and Electrical Engineering
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The Mumford-Shah functional is a general and quite popular variational model for image segmentation. In particular, it provides the possibility to represent regions by smooth approximations. In this paper, we derive a statistical interpretation of the full (piecewise smooth) Mumford-Shah functional by relating it to recent works on local region statistics. Moreover, we show that this statistical interpretation comes along with several implications. Firstly, one can derive extended versions of the Mumford-Shah functional including more general distribution models. Secondly, it leads to faster implementations. Finally, thanks to the analytical expression of the smooth approximation via Gaussian convolution, the coordinate descent can be replaced by a true gradient descent.