Multiscale 3D feature extraction and matching with an application to 3D face recognition

Keywords: 3D feature extraction 3D shape matching 3D face recognition Heat equation Mesh signal processing a b s t r a c t We present a new multiscale surface representation for 3D shape matching that is based on scale-space theory. The representation, Curvature Scale-Space 3D (CS3), is well-suited for measuring dissimilarity between (partial) surfaces having unknown position, orientation, and scale. The CS3 representation is obtained by evolving the surface curvatures according to the heat equation. This evolution process yields a stack of increasingly smoothed surface curvatures that is useful for keypoint extraction and descriptor computations. We augment this information with an associated scale parameter at each stack level to define our mul-tiscale CS3 surface representation. The scale parameter is necessary for automatic scale selection, which has proven to be successful in 2D scale-invariant shape matching applications. We show that our keypoint and descriptor computation approach outperforms many of the leading methods. The main advantages of our representation are its computational efficiency, lower memory requirements, and ease of implementation. 3D shape matching refers to the process of measuring the amount of dissimilarity between 3D shapes [1]. Partial shape matching is considered to be a more difficult subproblem, where the dissimilarity is measured between partial regions on input surfaces, and the relative position, orientation, scale, or extent of the overlap is unknown [2]. The main difficulties faced by 3D surface matching systems are Representation issues: the arbitrary organization of points in 3D makes the processing of input surfaces more difficult than processing signals in R n , where the data are generally organized in the form a grid. This and the non-Euclidean geometry of the surface hinder design of efficient matching algorithms. Geometric transformations: the input surfaces may have arbitrary translation, rotation, and scale. They may also have undergone non-rigid transformations. Non-geometric transformations: the surfaces may have been perturbed with varying levels of noise, contain topological noise, or have different sampling variations. A large number of 3D shape matching techniques already exist in the literature [1,3]; each approach generally addresses a subset of the above-mentioned difficulties. We present a new 3D surface matching approach motivated by the scale-space theory of signals, which was specifically developed to deal with noise and differences in resolution and scale. We propose a surface representation, which is stable against surface noise, and can be used to form discriminative feature vectors useful for establishing correspondences between regions on …