Name
Abstract | ||
|---|---|---|
In a previously reported work, a distance function was proposed which defines the distance between any pair of points as the weighted sum of their ordered coordinate differences. We call this distance function in this work as linear combination form of weighted distance (LWD), and observe that if an LWD is a norm, it can be expressed in an equivalent form, which is associated with a chamfering mask. We refer to this class of distance functions as chamfering weighted distances (CWD). In this work, properties of hyperspheres of CWDs in arbitrary dimension are discussed. We have derived expressions for the vertices, surface areas and volumes of n-D hyperspheres. These are used in defining geometric error measures to study the proximity of these distance functions to Euclidean metrics. We have also used other analytical error measures to consider their suitability in approximating Euclidean distances. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.1016/j.patrec.2012.09.011 | Pattern Recognition Letters |
Keywords | Field | DocType |
analytical error measure,chamfering mask,linear combination form,weighted sum,equivalent form,approximating euclidean distance,euclidean metrics,weighted distance,arbitrary dimension,geometric error measure,distance function,hypersphere,euclidean distance | Linear combination,Combinatorics,Minkowski distance,Euclidean distance,Metric (mathematics),Hypersphere,Distance matrix,Weighted Voronoi diagram,Mathematics,Euclidean distance matrix | Journal |
Volume | Issue | ISSN |
34 | 2 | 0167-8655 |
Citations | PageRank | References |
5 | 0.46 | 16 |
Authors | ||
1 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jayanta Mukherjee | 1 | 378 | 56.06 |