Unsupervised Non-parametric Region Segmentation Using Level Sets

We present a novel non-parametric unsupervised segmentation algorithm based on Region Competition [21]; but implemented within a Level Sets framework [11]. The key novelty of the algorithm is that it can solve N ≥ 2 class segmentation problems using just one embedded surface; this is achieved by controlling the merging and splitting behaviour of the level sets according to a Minimum Description Length (MDL) [6, 14] cost function. This is in contrast to N class region-based Level Set segmentation methods to date which operate by evolving multiple coupled embedded surfaces in parallel [3, 13, 20]. Furthermore, it operates in an unsupervised manner; it is necessary neither to specify the value of N nor the class models a-priori. We argue that the Level Sets methodology provides a more convenient framework for the implementation of the Region Competition algorithm, which is conventionally implemented using region membership arrays due to the lack of a intrinsic curve representation. Finally, we generalise the Gaussian region model used in standard Region Competition to the non-parametric case. The region boundary motion and merge equations become simple expressions containing cross-entropy and entropy terms.