Modeling the structure of multivariate manifolds: Shape maps

We propose a shape population metric that reflects the interdependencies between points observed in a set of examples. It provides a notion of topology for shape and appearance models that represents the behavior of individual observations in a metric space, in which distances between points correspond to their joint modeling properties. A Markov chain is learnt using the description lengths of models that describe sub sets of the entire data. The according diffusion map or shape map provides for the metric that reflects the behavior of the training population. With this metric functional clustering, deformation- or motion segmentation, sparse sampling and the treatment of outliers can be dealt with in a unified and transparent manner. We report experimental results on synthetic and real world data and compare the framework with existing specialized approaches. 1