RBF Shape Histograms and Their Application to 3D Face Processing

We present novel, pose invariant 3D shape descriptors and we test the performance of these descriptors, when applied to the problems of nose identification and localisation in 3D face data. We generate an implicit radial basis function (RBF) model of the facial surface and construction of our novel features is based on sampling this RBF model over a set of concentric spheres to give a spherically-sampled RBF (SSR) histogram. In addition to providing a feature identification mechanism, SSR histograms can be processed, with very little computational overhead, to estimate the volumetric intersection of the object (face) and a bounding sphere, centred on any object surface point. A minimisation of this volume, at an appropriate scale, can be used to both define and localise the facial nose tip to an arbitrary resolution. We test our descriptors on a subset of the particularly challenging University of York 3D face database. This data set consists of 1736 3D faces, with facial expression variations, pose variations, data spikes and missing parts. Noses vertices are identified at a rate of 99.6% on unseen subjects and our approach significantly outperforms three variants of spin images.