Reconstructing the Complete 3D Shape of Faces from Partial Information (Rekonstruktion der dreidimensionalen Form von Gesichtern aus partieller Information)

Abstract

Based on the assumption that a class of objects or data can be represented as a vector space spanned by a set of examples, we present a general method to estimate vector components of a novel vector, given only a subset of its dimensions. We apply this method to recover 3D shape of human faces from 2D image positions of a small number of feature points. The application demonstrates two aspects of the estimation of novel vector components: (1) From 2D image positions, we estimate 3D coordinates, and (2) from a small set of points, we obtain vertex positions of a high-resolution surface mesh. We provide an evaluation of the technique on laser scans of faces, and present an example of 3D shape reconstruction from a photograph. Our technique involves a tradeoff between reconstruction of the given measurements, and plausibility of the result. This is achieved in a Bayesian approach, and with a statistical analysis of the examples.