<span lang="EN-US">Gender and ethnicity classifications are a long-standing challenge in the face recognition’s field. They key-demographic traits of individuals applied real-world applications such as biometric demographic research, human-computer interaction (HCI), law enforcement online advertisements. Thus, many methods have been proposed to address gender or/and race achieved various...

6 Let P be a closed simple polygon with n vertices. For any two points in P , the geodesic 7 distance between them is the length of the shortest path that connects them among all 8 paths contained in P . The geodesic center of P is the unique point in P that minimizes the 9 largest geodesic distance to all other points of P . In 1989, Pollack, Sharir and Rote [Disc. 10 & Comput. Geom. 89] showe...

We study Sobolev-type metrics of fractional order on the group of compactly supported diffeomorphisms Diffc(M), where M is a Riemannian manifold of bounded geometry. We prove that the geodesic distance, induced by the Riemannian metric, vanishes if the order s satisfies 0 ≤ s < 1 2 . For M 6= R we show the vanishing of the geodesic distance also for s = 1 2 , and for dim(M) = 1 we show that the...

We investigate the higher-order Voronoi diagrams of n point sites with respect to the geodesic distance in a simple polygon with h > 0 polygonal holes and c corners. Given a set of n point sites, the korder Voronoi diagram partitions the plane into several regions such that all points in a region share the same k nearest sites. The nearest-site (first-order) geodesic Voronoi diagram has already...

We find a different approach to define convex functions in the subRiemannian setting. A function on a sub-Riemannian manifold is nonholonomically geodesic convex if its restriction to any nonholonomic (straightest) geodesic is convex. In the case of Carnot groups, this definition coincides with that by Danniell-Garofalo-Nieuhn (equivalent to that by Lu-Manfredi-Stroffolini). Nonholonomic geodes...