Segmenting an image into distinct, meaningful regions is thought to be largely a task in early visual processing, involving low-level processes: local, numerical and bottom-up. Most segmenting algorithms can be broadly divided into categories based on opposing strategies: local, edge-operator methods and region-based, histogram methods. A recent algorithm developed by S. and D. Geman uses ideas from statistical mechanics to divide up an image into maximally homogeneous regions with shortest possible boundaries. The approach used in this research is inspired by Geman's work and involves segmenting by minimizing energy functionals. These functionals reflect properties that one would expect of any segmenting scheme. Preliminary work shows that the Geman scheme can be thought of as a continuous spectrum of methods bridging edge-operator methods and region- based methods. The research in this project will be focussed along three lines: 1) Theoretical investgation regarding the existence and smoothness of solutions, 2) Extension to multi-grid relaxation and related questions of shape representation, and; 3) Extension to segmentation based on image features other than or in addition to the gray level.
