Synthesis, Deformation, and Statistics of 3D Objects via M-Reps

Abstract

The m-rep, a representation of the interior of one or more objects, from which boundaries can be synthesized, is described in detail. An m-rep consists of sheets of medial atoms; both sampled and parametrized representations of these sheets are described. Means of forming objects made from a main sheet (figure) and attached protrusion or indentation subfigures are described, as are multiscale hierarchies of object complexes, objects, figures, atoms, and voxels. The object-relative coordinate system provided by m-reps is presented. To allow the estimation of probabilities on populations of m-reps, the m-rep can be understood as an element in a feature space that takes the mathematical form of a symmetric space. Doing this provides the ability to estimate probabilities by a generalization of principal component analysis to these curved spaces.