Image segmentation by iterative optimization of multiphase multiple piecewise constant model and Four-Color relabeling

In the paper an iteratively unsupervised image segmentation algorithm is developed, which is based on our proposed multiphase multiple piecewise constant (MMPC) model and its graph cuts optimization. The MMPC model use multiple constants to model each phase instead of one single constant used in Chan and Vese (CV) model and cartoon limit so that heterogeneous image object segmentation can be effectively dealt with. We show that the multiphase optimization problem based on our proposed model can be approximately solved by graph cuts methods. Four-Color theorem is used to relabel the regions of image after every iteration, which makes it possible to represent and segment an arbitrary number of regions in image with only four phases. Therefore, the computational cost and memory usage are greatly reduced. The comparison with some typical unsupervised image segmentation methods using a large number of images from the Berkeley Segmentation Dataset demonstrates the proposed algorithm can effectively segment natural images with a good performance and acceptable computational time.