The Virasoro-Bott group endowed with the right-invariant L2metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.

In this paper, we show that the L1 geodesic diameter and center of a simple polygon can be computed in linear time. For the purpose, we focus on revealing basic geometric properties of the L1 geodesic balls, that is, the metric balls with respect to the L1 geodesic distance. More specifically, in this paper we show that any family of L1 geodesic balls in any simple polygon has Helly number two,...

Abstract—In this paper, we present a comparative study of three methods of 2D face recognition system such as: Iso-Geodesic Curves (IGC), Geodesic Distance (GD) and Geodesic-Intensity Histogram (GIH). These approaches are based on computing of geodesic distance between points of facial surface and between facial curves. In this study we represented the image at gray level as a 2D surface in a 3...

In this paper, we investigate the L1 geodesic farthest neighbors in a simple polygon P , and address several fundamental problems related to farthest neighbors. Given a subset S ⊆ P , an L1 geodesic farthest neighbor of p ∈ P from S is one that maximizes the length of L1 shortest path from p in P . Our list of problems include: computing the diameter, radius, center, farthestneighbor Voronoi di...

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

For any two points in a simple polygon P , the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regi...

<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...