Embedded Profile Hidden Markov Models for Shape Analysis

An ideal shape model should be both invariant to global transformations and robust to local distortions. In this paper we present a new shape modeling framework that achieves both efficiently. A shape instance is described by a curvature-based shape descriptor. A Profile Hidden Markov Model (PHMM) is then built on such descriptors to repre-sent a class of similar shapes. PHMMs are a particular type of Hidden Markov Models (HMMs) with special states and architecture that can tolerate considerable shape con-tour perturbations, including rigid and non-rigid deforma-tions, occlusions, and missing parts. The sparseness of the PHMM structure provides efficient inference and learning algorithms for shape modeling and analysis. To capture the global characteristics of a class of shapes, the PHMM pa-rameters are further embedded into a subspace that models long term spatial dependencies. The new framework can be applied to a wide range of problems, such as shape match-ing/registration, classification/recognition, etc. Our experi-mental results demonstrate the effectiveness and robustness of this new model in these different settings. 1