We propose a new definition of geodesic completeness, based on analytical continuation in the complex domain: we apply this idea to Clifton-Pohl torus, relating, for each geodesic, completeness to the value of a function of initial conditions, called ’impulse’.

We study the properties of geodesic currents on free groups, particularly the " intersection form " that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces .

We study the properties of geodesic currents on free groups, particularly the " intersection form " that is similar to Bonahon's notion of the intersection number between geodesic currents on hyperbolic surfaces .

Principal Author’s Biography Shalini Gupta received a BE degree in Electronics and Electrical Communication Engineering from Punjab Engineering College, India. She received a MS degree in Electrical and Computer Engineering from the University of Texas at Austin, where she is currently a PhD student. During her masters, she developed techniques for computer aided diagnosis of breast cancer. She...

We have developed an algorithm to generate a complete map of the traversable region for a personal assistant robot using monocular vision only. Using multiple taken by a simple webcam, obstacle detection and avoidance algorithms have been developed. Simple Linear Iterative Clustering (SLIC) has been used for segmentation to reduce the memory and computation cost. A simple mapping technique usin...

We study how convergence of an observer whose state lives in a copy of the given system’s space can be established using a Riemannian metric. We show that the existence of an observer guaranteeing the property that a Riemannian distance between system and observer solutions is nonincreasing implies that the Lie derivative of the Riemannian metric along the system vector field is conditionally n...

Given a polygon P , for two points s and t contained in the polygon, their geodesic distance is the length of the shortest st-path within P . A geodesic disk of radius r centered at a point v ∈ P is the set of points in P whose geodesic distance to v is at most r. We present a polynomial time 2-approximation algorithm for finding a densest geodesic unit disk packing in P . Allowing arbitrary ra...

The problem of interactive foreground/background segmentation in still images is of great practical importance in image editing. They avoid the boundary-length bias of graph-cut methods and results in increased sensitivity to seed placement. A new proposed method of fully automatic processing frameworks is given based on Graph-cut and Geodesic Graph cut algorithms. This paper addresses the prob...

In this article, the totally geodesic submanifolds in the complex 2Grassmannian G2(C) and in the quaternionic 2-Grassmannian G2(H) are classified. It turns out that for both of these spaces, the earlier classification of maximal totally geodesic submanifolds in Riemannian symmetric spaces of rank 2 published by Chen and Nagano (1978) is incomplete. For example, G2(H) with n ≥ 5 contains totally...

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...