Modelling surface normal distribution using the azimuthal equidistant projection

Authors:
William A. P. Smith;Edwin R. Hancock
Affiliations:
Department of Computer Science, The University of York, York, UK;Department of Computer Science, The University of York, York, UK
Venue:
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Year:
2005

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Abstract

This paper describes how surface shape, and in particular facial shape, can be modeled using a statistical model that captures variations in surface normal direction. To construct this model we make use of the azimuthal equidistant projection to map surface normals from the unit sphere to points on a local tangent plane. The variations in surface normal direction are captured using the covariance matrix for the projected point positions. This allows us to model variations in surface shape using a standard point distribution model. We show how this model can be trained using surface normal data acquired from range images. We fit the model to intensity data using constraints on the surface normal direction provided by Lambert's law. We demonstrate the utility of the method on the recovery of 3D surface shape from 2D images.