In this paper, we compare two different definitions of distance transform for gray level images: the Gray Weighted Distance Transform (GWDT), and the Weighted Distance Transform On Curved Space (WDTOCS). We show through theoretical and experimental comparisons the differences, the strengths and the weaknesses of these two distances. Continuous case D GW DT = 1 0 |π(t)|dt.

The distance covariance of Sz\'ekely, et al. [23] and Sz\'ekely Rizzo [21], a powerful measure dependence between sets multivariate random variables, has the crucial feature that it equals zero if only are mutually independent. Hence can be applied to data detect arbitrary types non-linear associations variables. We provide in this article basic, albeit rigorous, introductory treatment covarian...

‎The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$‎. ‎In this case‎, ‎$B$ is called a textit{metric basis} for $G$‎. ‎The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$‎. ‎Givi...

This paper deals with the basic notions of k-tautimmersions . These notions come from two special cases; that is, tight and taut immersions. Tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. We generalize hight and distance functions to cylindrical function and define basic notions of k-taut ...

this paper deals with the basic notions of k-tautimmersions . these notions come from two special cases; that is, tight and taut immersions. tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. we generalize hight and distance functions to cylindrical function and define basic notions of k-taut im...

distance-balanced graphs are introduced as graphs in which every edge uv has the followingproperty: the number of vertices closer to u than to v is equal to the number of vertices closerto v than to u. basic properties of these graphs are obtained. in this paper, we study theconditions under which some graph operations produce a distance-balanced graph.