A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
International Journal of Computer Vision
A Convex Formulation of Continuous Multi-label Problems
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part III
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
Exact optimization for Markov random fields with convex priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
A convex representation for the vectorial Mumford-Shah functional
CVPR '12 Proceedings of the 2012 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
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The geometric active contour model is a popular method for computing the segmentation of an image into two phases, based on Mumford-Shah model. The main problem in image segmentation based this method may lead to non-convex minimization problems that it difficult to obtain a global solution. In this paper, we propose a convex relaxation of the popular K-means algorithm. Our approach is based on the vector-valued relaxation technique developed by Brown et al. (UCLA CAM Report 10-43, 2010) and Goldstein et al. (UCLA CAM Report 09-77, 2009). We applied the proposed framework to multi-object extraction problems on remote sensing images. We provide several experimental results to demonstrate that our convex model yields global solutions to the well known Mumford-Shah model.