Hyperbolic polyhedral surfaces with regular faces

We study hyperbolic polyhedral surfaces with faces isometric to regular hyperbolic polygons satisfying that the total angles at vertices are at least $2\pi.$ The combinatorial information of these surfaces is shown to be identified with that of Euclidean polyhedral surfaces with negative combinatorial curvature everywhere. We prove that there is a gap between areas of non-smooth hyperbolic polyhedral surfaces and the area of smooth hyperbolic surfaces. The numerical result for the gap is obtained for hyperbolic polyhedral surfaces, homeomorphic to the double torus, whose 1-skeletons are cubic graphs.Comment: 23 pages, 3 figures. arXiv admin note: text overlap with arXiv:1804.1103

3-D Shape Matching for Face Analysis and Recognition

The aims of this paper are to introduce a 3-D shape matching scheme for automatic face recognition and to demonstrate its invariance to pose and facial expressions. The core of this scheme lies on the combination of non-rigid deformation registration and statistical shape modelling. While the former matches 3-D faces regardless of facial expression variations, the latter provides a low-dimensional feature vector that describes the deformation after the shape matching process, thereby enabling robust identification of 3-D faces. In order to assist establishment of accurate dense point correspondences, an isometric embedding shape representation is introduced, which is able to transform 3-D faces to a canonical form that retains the intrinsic geometric structure and achieve shape alignment of 3-D faces independent from individual’s facial expression. The feasibility and effectiveness of the proposed method was investigated using standard publicly available Gavab and BU-3DFE databases, which contain faces expressions and pose variations. The performance of the system was compared with the existing benchmark approaches and it demonstrates that the proposed scheme provides a competitive solution for the face recognition task with real-world practicality