This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are computed as the shortest paths between superpixels via their boundaries. We also incorporate adaptive voting weights and spatial pyramid configurations to include s...

We give a new simple construction of the maximal entropy invariant measure (the Bowen{Margulis measure) for the geodesic ow on a compact negatively curved manifold. This construction directly connects invariant`conformal density" arising from the Patterson measure on the sphere at innnity of the universal covering space with the maximal entropy measureof the geodesic ow. 0. Introduction Let M b...

When a Hamiltonian system has a \Kinetic + Potential" structure, the resulting ow is locally a geodesic ow. But there may be singularities of the geodesic structure, so the local structure does not always imply that the ow is globally a geodesic ow. In order for a ow to be a geodesic ow, the underlying manifold must have the structure of a unit tangent bundle. We develop homological conditions ...

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,...

In this paper we will survey some recent results on the Hamiltonian dynamics of the geodesic flow of a Riemannian manifold. More specifically, we are interested in those manifolds which admit a Riemannian metric for which the geodesic flow is integrable. In Section 2, we introduce the necessary topics from symplectic geometry and Hamiltonian dynamics (and, in particular, we defined the terms ge...

We show that an invariant surface allows to construct the Jacobi vector field along a geodesic and construct the formula for the normal component of the Jacobi field. If a geodesic is the transversal intersection of two invariant surfaces (such situation we have, for example, if the geodesic is hyperbolic), then we can construct a fundamental solution of the the Jacobi-Hill equation ü = −K(u)u....

The S2×R geometry is derived by direct product of the spherical plane S2 and the real line R. In [9] the third author has determined the geodesic curves, geodesic balls of S2×R space, computed their volume and defined the notion of the geodesic ball packing and its density. Moreover, he has developed a procedure to determine the density of the geodesic ball packing for generalized Coxeter space...

A shortest path connecting two vertices u and v is called a u-v geodesic. The distance between u and v, denoted by dG(u, v), is the number of edges in a u-v geodesic. A graph G with n vertices is geodesic-pancyclic if for each pair of vertices u, v ∈ V (G), every u-v geodesic lies on every cycle of length k satisfying max{2dG(u, v), 3} ≤ k ≤ n. In this paper, we study the properties for graphs ...

It is shown that every non-compact hyperbolic manifold of finite volume has a finite cover admitting a geodesic ideal triangulation. Also, every hyperbolic manifold of finite volume with non-empty, totally geodesic boundary has a finite regular cover which has a geodesic partially truncated triangulation. The proofs use an extension of a result due to Long and Niblo concerning the separability ...

For a pair of vertices u, v ∈ V (G), a cycle is called a geodesic cycle with u and v if a shortest path of G joining u and v lies on the cycle. A graph G is pancyclic [12] if it contains a cycle of every length from 3 to |V (G)| inclusive. Furthermore, a graph G is called geodesic k-pancyclic [3] if for each pair of vertices u, v ∈ V (G), it contains a geodesic cycle of every integer length of ...