# geodesic distance

## geodesic distance

[¦jē·ə¦des·ik ′di·stəns]
(mathematics)
For two points in a Riemannian manifold, the length of a geodesic connecting them.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Surface-based algorithms generally segment a mesh by using geometric properties of the surface, such as the dihedral angles, geodesic distance and curvature.
The second metric is based on the notion of geodesic distance between a reference point and the desired point of interest on the body.
Use the shortest path method to calculate the geodesic distance [d.sub.ij] and to form the geodesic distance matrix [D.sup.2], in which [D.sup.2.sub.ij] = [absolute value of ([d.sup.2.sub.ij])] [member of] [R.sup.NxN].
However, the geodesic distance between pick-up and drop-off positions provided a suitable proxy.
Pretests showed that for both countries, the seeds captured the mainstream of the debate and formed an integral part of it, as measured by their average geodesic distance (see Appendix 2).
The geodesic length between those nodes is referred to as geodesic distance. In strengths of ties measures, the distance between two nodes defines the strengths of the shortest path between them (Suerdem and Bicquelet, 2014).
In this way, statistical and structural information of background can be fully exploited to construct background distribution, which would allow for a subsequently more accurate saliency measurement, and (2) we propose a new refinement framework, which is composed of edge-preserving element-level filtering and upsampling based on geodesic distance. The new refinement framework has an excellent ability to uniformly highlight the salient object and removing background noise.
The local topological properties of an iWordNet include vertices (nodes, words, etc.), degrees, clusters, betweenness centrality, closeness centrality, eigenvalue centrality, PageRank, geodesic distance, and "top items." The global topological properties include number of vertices, number of edges, number of components, number of clusters, clustering coefficient, mean geodesic distance, mean closeness centrality, mean closeness centrality, number of unique edges, graph density, and any variables derived from these variables.
[eta] = log(q) [member of] g is the exponential coordinates of the element q [member of] G, and the geodesic distance between the element q [member of] G and identity e [member of] G can be given by the metric of the exponential coordinates [mathematical expression not reproducible].
The geodesic distance between two nodes in a tree is equal to the number of links in the shortest path.
It substitutes Euclidean distance in MDS for geodesic distance. Hindered by MDS and geodesic distance computation, Isomap would become very time-consuming as the amount of the input data increases.
In this paper, we present the fully automatic and fast segmentation method of the ascending aorta from the CCTA image using a geodesic distance algorithm combined with a Hough transform.

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