A Markov Random Field Approach to Multi-scale Shape Analysis

Characterizing the geometric conformation of object complexes requires the description of certain geometric features. These features are most intuitive and provide locality if each is at a restricted range of scale. Thus a complete representation of a geometric entity, such as an object, includes descriptions at multiple scale levels, each describing a residue from the information provided at the larger scales. We have been developing a methodology using medial representations for 3D geometric entities. In this framework, we represent these entities at the following natural discrete scale levels: a whole object complex, individual objects, various object parts and sections, and fine boundary details. This has been proven to be a robust representation of the geometry scale space. It is particularly useful for probabilistic characterization that describes both the common geometry of a population of object complexes and the variation of instances within the population. Using our medial representation, we build Markov random field (MRF) models on the geometry scale space based on the statistics of shape residue across scales and between neighboring geometric entities at the level of locality given by its scale. In this paper, we present how to design MRF models on two scale levels, namely boundary displacement and object sections. This approach can be applied to various applications in medical image analysis such as image segmentation and object discrimination into classes.