Combinatorial Optimization of the piecewise constant Mumford-Shah functional with application to scalar/vector valued and volumetric image segmentation

The Piecewise Smooth Mumford-Shah Functional on an Arbitrary Graph

The Mumford-Shah functional has had a major impact on a variety of image analysis problems, including image segmentation and filtering, and, despite being introduced over two decades ago, it is still in widespread use. Present day optimization of the Mumford-Shah functional is predominated by active contour methods. Until recently, these formulations necessitated optimization of the contour by ...

Variational image segmentation model coupled with image restoration achievements

Image segmentation and image restoration are two important topics in image processing with great achievements. In this paper, we propose a new multiphase segmentation model by combining image restoration and image segmentation models. Utilizing image restoration aspects, the proposed segmentation model can effectively and robustly tackle high noisy images, blurry images, images with missing pix...

Image segmentation using level sets and the piecewise-constant Mumford-Shah model

A Piecewise Constant Region Based Simultaneous Image Segmentation and Registration

A new variational region based model for a simultaneous image segmentation and a rigid registration is proposed. The purpose of the model is to segment and register novel images simultaneously using a modified piecewise constant Mumford-Shah functional and region intensity values. The segmentation is obtained by minimizing a modified piecewise constant Mumford-Shah functional. A registration is...

Hierarchical Mumford-Shah Model for Vector-valued Image Segmentation, Denoising and Reconstruction

A novel hierarchical Mumford-Shah functional model is addressed to simultaneously segment, denoise and reconstruct the data within a given vector-valued image such as a color image, and to handle important image features such as triple points and other multiple junctions, which can be seen as a hierarchical case of the Mumford-Shah minimal partition problem for vector-valued images. At the same...