Motivated by the work of Asano et al. [1], we consider the distance trisector problem and zone diagram considering segments in the plane as the input geometric objects. As the most basic case, we first consider the pair of curves (distance trisector curves) trisecting the distance between a point and a line, as shown in Figure 1. This is a natural extension of the bisector curve (that is a para...

We suggest a new color distance based on two observations. First, perceptual color differences were designed to be used to compare very similar colors. They do not capture human perception for medium and large color differences well. Thresholding was proposed to solve the problem for large color differences, i.e. two totally different colors are always the same distance apart. We show that thre...

Histograms are ubiquitous tools in numerous machine learning and computer vision tasks. It is common practice to use distances such as L2 for comparing histograms. This practice assumes that the histogram domains are aligned. However this assumption is violated through quantization, shape deformation, light changes, etc. The Earth Mover’s Distance (EMD) [12] is a cross-bin distance that address...

A real-time interactive distance lecture is a joint work that should be accomplished by the effort of the lecturer and his students in remote sites. It is important for the lecturer to get understanding information from the students which cannot be efficiently collected by only using video/audio channels between the lecturer and the students. This article proposes RIDEE-UIM (Understanding Infor...

a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.

We introduce a general framework for reasoning with prioritized data by aggregation of distance functions, study some basic properties of the entailment relations that are obtained, and relate them to other approaches for maintaining uncertain information.

As a generalization of Deza graphs, we introduce Deza digraphs and describe the basic theory of these graphs. We also prove the necessary and sufficient conditions when a weakly distance-regular digraph is a Deza digraph.

This document provides the foundations behind the functionality provided by the ρG library 1 , focusing on the basic operations the library provides: subsumption, refinement of directed labeled graphs, and distance/similarity assessment between directed labeled graphs.

In this paper, we describe fuzzy agglomerative clustering, a brand new fuzzy clustering algorithm. The basic idea of the proposed algorithm is based on the well-known hierarchical clustering methods. To achieve the soft or fuzzy output of the hierarchical clustering, we combine the single-linkage and completelinkage strategy together with a fuzzy distance. As the algorithm was created recently,...

Originating from specific requirements of future Advanced Driving Assistance Systems, the VIDA system offers both basic functionalities and advanced applications. Functionalities such as Lane Departure Warning and Safety Distance Warning are provided by the basic VIDA-W. On the same hardware platform and with the same sensing device, additional features can be added as plug-ins directly interfa...