3D Face Recognition in Continuous Spaces Francisco Jos´ e Silva Mata 1 , Elaine Grenot Castellanos 1 , Alfredo Mu˜ noz-Brise˜ no 1 , Isneri Talavera-Bustamante 1 , and Stefano Berretti 2(B ) 1 CENATAV, Havana, Cuba 2 University of Florence, Florence, Italy stefano.berretti@unifi.it Abstract. This work introduces a new approach for face recognition based on 3D scans. The main idea of the proposed method is that of converting the 3D face scans into a functional representation, perform- ing all the subsequent processing in the continuous space. To this end, a model alignment problem is first solved by combining graph matching and clustering. Fiducial points of the face are initially detected by analy- sis of continuous functions computed on the surface. Then, the alignment is performed by transforming the geometric graphs whose nodes are the critical points of the representative function of the surface in previously determined subspaces. A clustering step is finally applied to correct small displacement in the models. The 3D face representation is then obtained on the aligned models by functions carefully selected according to math- ematical and computational criteria. In particular, the face is divided into regions, which are treated as independent domains where a set of functions is determined by fitting the surface data using the least squares method. Experimental results demonstrate the feasibility of the method. Keywords: 3D face recognition · Functional representation 1 Introduction Models of the face acquired by 3D devices consist of dense point clouds, where points correspond to coordinates of the face surface discretely sampled by the capture device. For high resolution 3D scans, a very large number of points is typically used to represent the face, and triangular mesh representations are then derived to connect points in a structured way. However, this low level representation cannot be used directly to compare faces in recognition tasks, but appropriate descriptors that reduce the high dimensionality of points keeping, at the same time, salient features of the face should be derived. Face recognition using either high resolution or low-resolution 3D scans has received an increasing interest in the last few years (for a thorough discussion of existing methods we refer to the survey in [7] and the literature review in [3, 18]). In general, 3D face recognition approaches proposed in the literature can be grouped as global (or holistic ), and local (or region-based ). Hybrid approaches c  Springer International Publishing AG 2017 S. Battiato et al. (Eds.): ICIAP 2017, Part II, LNCS 10485, pp. 3–13, 2017. https://doi.org/10.1007/978-3-319-68548-9 1