Kinds Of Edges Research Articles

Edge Grouping Combining Boundary and Region Information

This paper introduces a new edge-grouping method to detect perceptually salient structures in noisy images. Specifically, we define a new grouping cost function in a ratio form, where the numerator measures the boundary proximity of the resulting structure and the denominator measures the area of the resulting structure. This area term introduces a preference towards detecting larger-size structures and, therefore, makes the resulting edge grouping more robust to image noise. To find the optimal edge grouping with the minimum grouping cost, we develop a special graph model with two different kinds of edges and then reduce the grouping problem to finding a special kind of cycle in this graph with a minimum cost in ratio form. This optimal cycle-finding problem can be solved in polynomial time by a previously developed graph algorithm. We implement this edge-grouping method, test it on both synthetic data and real images, and compare its performance against several available edge-grouping and edge-linking methods. Furthermore, we discuss several extensions of the proposed method, including the incorporation of the well-known grouping cues of continuity and intensity homogeneity, introducing a factor to balance the contributions from the boundary and region information, and the prevention of detecting self-intersecting boundaries.

Detecting induced subgraphs

Abstract An s-graph is a graph with two kind of edges: subdivisible edges and real edges. A realisation of an s-graph B is any graph obtained by subdividing subdivisible edges of B into paths of length at least one. Given an s-graph B, we study the decision problem Π B . Its instance is any graph G, its question is “Does G contains a realisation of B as an induced subgraph ?”. For several B's, the complexity is known and here we give the complexity for several more. We also provide results on the problem of detecting an induced cycle through two prescribed vertices. Download : Download full-size image Fig. 1 . S-graphs yielding trivially polynomial problems Download : Download full-size image Fig. 2 . Pyramids, prisms and thetas

Taxonomy of periodic nets and the design of materials

The concept of a natural tiling for a periodic net is introduced and used to derive a transitivity associated with the structure. It is accordingly shown that the transitivity provides a useful method of classifying polyhedra and nets. For design of materials to serve as targets for synthesis, structures with one kind of edge (edge transitive) are particularly important. Edge-transitive polyhedra, layers and 3-periodic nets are then described. Some other nets of special importance in crystal chemistry are also identified.

Three-periodic nets and tilings: edge-transitive binodal structures

28 three-periodic nets with two kinds of vertex and one kind of edge are identified. Some of their crystallographic properties and their natural tilings are described. Restrictions on site symmetry and coordination number of such nets are discussed and examples of their occurrence in crystal structures are given.

The row incompatibility and complement graph - A Novel concept of graph for logic synthesis

The paper presents a new concept of graph - the Row Incompatibility and Complement Graph. The idea was developed as a part of a new decomposition algorithm dedicated for PAL-based CPLD-s. A specific feature of the graph is that it contains two kinds of edges: connecting mutually incompatible nodes, and connecting mutually complementing nodes. The graph can be useful in certain class of optimization problems, in which compatibility of bit patterns in both the true and the complemented form has to be analyzed. Appropriate algorithms for the graph building and coloring are also presented.

Enumerative aspects of secondary structures

A secondary structure is a planar, labeled graph on the vertex set {1,…, n} having two kind of edges: the segments [ i, i+1], for 1⩽ i⩽ n−1 and arcs in the upper half-plane connecting some vertices i, j, i⩽ j, where j− i> l, for some fixed integer l. Any two arcs must be totally disjoint. We enumerate secondary structures with respect to their size n, rank l and order k (number of arcs), obtaining recursions and, in some cases, explicit formulae in terms of Motzkin, Catalan, and Narayana numbers. We give the asymptotics for the enumerating sequences and prove their log-convexity, log-concavity and unimodality. It is shown how these structures are connected with hypergeometric functions and orthogonal polynomials.

Three-periodic nets and tilings: semiregular nets.

Three-periodic semiregular nets are defined as those with just one kind of vertex and one kind of edge, but excluding the five regular and one quasiregular nets described earlier. Fourteen of these and their natural tilings are described and their importance in crystal chemistry is indicated.

Three-periodic nets and tilings: regular and quasiregular nets.

Regular nets are defined as those with symmetry that requires the coordination figure to be a regular polygon or polyhedron. It is shown that this definition leads to five regular 3-periodic nets. There is also one quasiregular net with a quasiregular coordination figure. The natural tiling of a net and its associated essential rings are also defined, and it is shown that the natural tilings of the regular nets have the property that there is just one kind of vertex, one kind of edge, one kind of ring and one kind of tile, i.e. transitivity 1111. The quasiregular net has two kinds of natural tile and transitivity 1112.

Nesting Success of a Disturbance‐Dependent Songbird on Different Kinds of Edges

We compared the nesting success of a disturbance‐dependent species, the Indigo Bunting ( Passerina cyanea), on different kinds of habitat edges in five sites (225 total nests) in southern Illinois from 1989 to 1993. Nest predation rates along agricultural and abrupt, permanent edges (e.g., wildlife openings, campgrounds) were nearly twice as high as rates along more gradual edges where plant succession was allowed to occur (e.g., treefalls, streamsides, gaps created by selective logging ). Levels of brood parasitism by Brown‐headed Cowbirds ( Molothrus ater) varied significantly among sites and years, but not among edge types. Clutch sizes, however, were significantly smaller at agricultural edges where nest predation rates were also high, which suggests either decreased food availability or a population dominated by younger and/or lower‐quality ( poor condition) birds. The results of this study illustrate the need to reevaluate management practices (e.g., wildlife openings) that are designed to promote populations of disturbance‐dependent wildlife.

A linear time algorithm for edge coloring of binomial trees

We consider the problem of efficient coloring of the edges of a so-called binomial tree T, i.e. acyclic graph containing two kinds of edges: those which must have a single color and those which are to be colored with L consecutive colors, where L is an arbitrary integer greater than 1. We give an O( n) time algorithm for optimal coloring of such a tree, where n is the number of vertices of T. Also, we give simple bounds on the chromatic index of T and a division of all binomial trees into two classes depending on their chromaticity.

Linear Dependencies Represented by Chain Graphs

Various special linear structures connected with covariance matrices are reviewed and graphical methods for their representation introduced, involving in particular two different kinds of edge between the nodes representing the component variables. The distinction between decomposable and nondecomposable structures is emphasized. Empirical examples are described for the main possibilities with four component variables.