We present a novel minimum ratio contour (MRC) algorithm, for discretely optimizing contours on the surface of triangle meshes. We compute the contour having the minimal ratio between a numerator and a denominator energy. The numerator energy measures the bending and salience (feature adaptation) of a contour, while the denominator energy measures contour length. Given an initial contour, the o...

We propose a new method for the encoding of label images (also known as segmentation maps or alpha planes) that are often used to identify object location in region-based image and video coders. The method is contour-based and lossless with a contour model composed of two parts: a contour graph describing the topology of the contour network and a directional chain code to deal with the geometri...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

in this paper, it was shown that , where  and , and , where  is not prime and , are od-characterizable.

Let G be a group. Recall that the intersection graph of subgroups of G is an undirected graph whose vertex set is the set of all nontrivial subgroups of G and distinct vertices H,K are joined by an edge in this graph if and only if the intersection of H and K is nontrivial. The aim of this article is to investigate the interplay between the group-theoretic properties of a finite group G and the...

A constrained contour is an outline of a region of interest, obtained by linking edges under the constraints of connectivity, smoothness, image context and subjective or user speciied constraints. We discuss a constrained contouring algorithm in polar coordinates to trace closed contours. The algorithm nds optimal contour locations in all radial direction according to the constraints of context...

This paper presents a very efficient method for vectorizing and labeling very large raster hypsographic map images. By extending the contour tree (Freeman and Morse, 1967) to a contour graph, open contour lines and carrying contour lines can be handled. The ambiguities of the topological relationships among contour lines are resolved using map structure information, i.e., elevation tags and ind...