An Efficient Bottom-Up Image Segmentation Method Based on Region Growing, Region Competition and the Mumford Shah Functional

Curve evolution implementations of the Mumford-Shah functional are of broad interest in image segmentation. These implementations, however, have initialization problems. A mathematical analysis of the initialization problem for the bi-modal Chan-Vese model is provided in this paper. The initialization problem is a result of the non-convexity of the Mumford-Shah functional and the top-down hierarchy of the model´s use of global region information in the image. An efficient image segmentation method is proposed that alleviates the initialization problem, based on region growing, region competition and the Mumford Shah functional. This algorithm is able to automatically and efficiently segment objects in complicated images. Using a bottom-up hierarchy, the method avoids the initialization problem in the Chan-Vese model and works for images with multiple junctions and color images. It can be extended to textured images. Experimental results show that the proposed method is robust to the effects of noise