Face Recognition Based on Manifold Learning and SVM Classification of 2D and 3D Geodesic Curves

Abstract

This chapter has a twofold objective. On the one hand, an original approach based on the computation of radial geodesic distances (RGD) is proposed to represent two-dimensional (2D) face images and three-dimensional (3D) face models for the purpose of face recognition. In 3D, the RGD of a generic point of a 3D face surface is computed as the length of the particular geodesic that connects the point with a reference point along a radial direction. In 2D, the RGD of a face image pixel with respect to a reference pixel accounts for the difference of gray level intensities of the two pixels and the Euclidean distance between them. The main contribution of this solution is to permit direct comparison between representations extracted from 2D and 3D facial data, thus opening the way to hybrid approaches for face recognition capable to combine and exploit advantages of different media so as to overcome limitations of traditional solutions based on 2D still images. On the other hand, face representations based on RGDs are used for the purpose of face identification by using them in an operative framework that exploits state of the art techniques for manifold embedding and machine learning. Due to the high dimensionality of face representations based on RGD, embedding into lower-dimensional spaces using manifold learning is applied before classification. Support Vector Machines (SVMs) are used to perform face recognition using 2D- and 3D-RGDs. This shows a general work flow that is not limited to face recognition applications, but can be used in many different contexts of recognition and retrieval. Experimental results are reported for 3D-3D and 2D-3D face recognition using the proposed approach.