Learning models of shape from three-dimensional range data

Constructing shape models of complex articulated and deformable objects is a fundamental capability that enables a variety of applications in computer graphics, biomechanics, arts and entertainment. Current approaches require a significant amount of manual intervention in the model construction process. In this thesis, we present algorithms for learning models of shape that reduce the need for human input. First, we describe an unsupervised algorithm for registering 3D surface scans of an object undergoing significant deformations. Our algorithm does not use markers, nor does it assume prior knowledge about object shape, the dynamics of its deformation, or scan alignment. It is based on a probabilistic model, which minimizes deformation and attempts to preserve geodesic distances and local mesh geometry. Second, we describe an algorithm whose input is a set of meshes corresponding to different configurations of an articulated object. The algorithm automatically recovers a decomposition of the object into approximately rigid parts, the location of the parts in the different object instances, and the articulated object skeleton linking the parts. We also address the problem of learning the space of human body deformations from 3D scans. Unlike existing example-based approaches, our model spans variation in both subject shape and pose. We learn a model of surface deformation as a function of the joint angles of the articulated human skeleton. We also learn a separate model of the variation between different body shapes. We show how to combine these two models to produce realistic deformation for different people in different poses. Finally, we show how our framework can be used for shape completion---generating a complete surface mesh given a limited set of markers specifying the target shape. We use this capability to complete partial mesh geometry and to animate marker motion capture sequences.