Showing papers on "Adjacency list published in 1983"

Segmentation by Texture Using Correlation

Abstract: The correlation coefficients are used for segmentation according to texture. They are first evaluated on a set of square regions forming two levels of the quadratic picture tree (or pyramid). If the coefficients of a square and its four children in the tree are similar, then that region is considered to be of uniform texture. If not, it is replaced by its children. In this way, the split-and-merge algorithm is used to achieve a preliminary segmentation. It is followed by a grouping algorithm using the correlation coefficients and the region adjacency graph, plus a small region elimination step. The latter regions are grouped according to their gray level because texture cannot be defined reliably on very small regions. Examples of implementation on four pictures are included.

Topology quasi-preservation by local parallel operations

Abstract: A set of local parallel operations on binary images, represented as sets of square lattice points is determined, whose members use 2 × 3 windows and do shrinking with the quasi-preservation of topological structures of the images. The adjacency tree is used to define the topology of the images, and is required to be ultimately reduced to the root node (background) by repeated elimination of the leaves which correspond to simply connected components. The set of operations is constructively obtained by determining necesary and sufficient conditions for a parallel operation to satisfy the quasi-preservation property thus defined.

An Approximation To The 3D Border (A3DB)

Abstract: Linear octtrees have been introduced recently1 as a data structure capable of compacting the ten fields normally required by an octtree's node into one. Operations like projection, superposition, adjacency, mapping from and to a 2n x 2n x 2n-digital array have also been described in the above reference. In this paper the authors propose an approximate solution to the determination of the 3D border of an object represented by a linear octtree. The corresponding algorithm is shown to be executable in O(nN) time and to require less than 4N memory locations, where N is the number of black nodes of the linear octtree, and n is the resolution of the binary image.© (1983) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Graphical Enumeration of Polyhedral Clusters

Abstract: The following hypothesis is proposed: crystal struc- tures may be ordered or classified according to the polymerization of those coordination polyhedra (not necessarily of the same type) with the higher bond valences. The linkage of polyhedra to form clusters is considered from a graph-theoretic viewpoint. Poly- hedra are represented by the chromatic vertices of a (labelled) graph, in which different colours indicate coordination polyhedra of different type. The linking together of polyhedra is denoted by the presence of an edge or edges between vertices representing linked polyhedra, the number of edges between two vertices corresponding to the number of corners (atoms) common to both polyhedra. Information on geo- metrical isomerism is lost in this graphical represen- tation, but the graphical characteristics are retained. The graph may be completely represented by its matrix, ann × nmatrix (with(~} = N adjacency \/-/ independent dements) denoting vertex linkage; it is convenient to represent the N independent matrix elements by the ordered set {a,b,c,...,N}. The collec- tion of all permutations of the vertex labellings that preserve isomorphism is called the automorphism group F(G) of the graph. F(G) is a subgroup of the symmetric group Sn, and the complementary disjoint subgroup of S, defines all distinct graphs whose vertex sets correspond to the (unordered) set {a,b,c,...,N}. However, it is more convenient in practice to work with the corresponding matrix-element symmetries that form

Some Connections Between Groups and Graphs. A Survey

Abstract: Publisher Summary One might consider a question that is more general than to represent an element of S n with the aid of transpositions—namely, to enumerate the distinct representations of any given element of an arbitrary finite group as a product whose elements are taken from an arbitrary given set of generators. One can easily carry out the graph-theoretical interpretation of super P-groups using Cayley graphs. Another combinatorial approach to simple groups is to study the lengths of the products that represent the identity element of a simple group. There are results and problems that are closely connected with the adjacency matrix of the Cayley graph of simple groups. It is of some interest to study how group-theoretical results can be applied to other branches of mathematics, for example, to graph theory.