Directional Statistics for Facial Shape-from Shading

Directional Statistics for Facial Shape-from Shading

Abstract

The recovery of facial shape using shape-from-shading is frustrated by concave-convex ambiguities, variable albedo and shadowing. In this talk I will show how these problems can be overcome by incorporating a statistical model for surface normal direction within the shape-from-shading process. The main contribution of the talk is to develop a representation of the distribution of surface normals. Two approaches are considered. The first of these draws on the equidistant azimuthal projection from cartography and transforms a distribution of surface normal direction on a unit sphere to a distribution of points on a tangent plane. The second approach generalises this idea to Riemannian manifolds and shows how the principal geodesic analysis on the exponential map can be used to model surface shape. We show how facial shape can be recovered by fitting the models to image brightness data using robust statistics. The error residuals can be used to estimate both facial albedo and the locations of facial shadows. Results are shown on the Yale B and CMU PIE databases.