Showing papers on "Adjacency list published in 1988"

Graph-based heuristics for recognition of machined features from a 3D solid model

Abstract: The internal representation of the solid modeller provides a description of parts which when used directly is useful for automation of the process planning function. So that the CAD model can be used to provide the information required for manufacturing, techniques to improve machine understanding of the part as required for manufacturing are needed. This paper presents the development of the concept attributed adjacency graph (AAG) for the recognition of machined features from a 3D boundary representation of a solid. Current implementation of the feature recogniser is limited to polyhedral features such as pockets, slots, steps, blind steps, blind slots, and polyhedral holes. Sample results that show the capabilities of the system are presented.

A hierarchical boundary model for solid object representation

Abstract: A new hierarchical model for solid object representation is described. This model, called a hierarchical face adjacency hypergraph (HFAH), is based on a relational description of the object boundary, called a face adjacency hypergraph (FAH), which considers faces as the primary topological entities defining the object boundary. The HFAH consists of a hierarchy of FAHs describing the decomposition of the boundary of an object into form features. In this paper the HFAH is described together with its internal encoding structure. Two basic transformations, called refinement and abstraction, are defined on the hierarchical model; these allow effective and efficient modifications of the hierarchical boundary model.

Learning by choice of internal representations

Abstract: We introduce a learning algorithm for multilayer neural networks composed of binary linear threshold elements. Whereas existing algorithms reduce the learning process to minimizing a cost function over the weights, our method treats the internal representations as the fundamental entities to be determined. Once a correct set of internal representations is arrived at, the weights are found by the local and biologically plausible Perceptron Learning Rule (PLR). We tested our learning algorithm on four problems: adjacency, symmetry, parity and combined symmetry-parity.

Establishment of functional relationships between product components in assembly database

Abstract: In an assembly environment, explicit interface information between the major part components is necessary to determine proper assembly plans, avoid undesirable interferences between parts, and achieve the required product function. A semantic association model (SAM∗)-based assembly database is proposed to organize this assembly-specific semantic information in a hierarchical structure in its subassembly module. A hybrid constructive solid geometry/boundary representation (as a structured face adjacency graph) is used to represent each component part of the assembly. These are stored in single part modules. The representational scheme is feature based and a functional relationship graph is developed to establish the required mating conditions between these features of different components in an assembly.

An efficient method to build early image description

Abstract: The elaboration of an early image description based on an adjacency graph of reliable regions is discussed. An optimal edge detector is used first to extract the contours of the analyzed scene. A topological-configuration-based look-up table is then used to determine the extremity points, and a closing-contours process is applied using gradient magnitude information. An efficient connected components labeling algorithm is used to segment the image into reliable regions. A region-based adjacency graph, where radiometric parameters and reliable polygonal approximation of region boundaries are associated with each node, is then created and used as an early image description of the analyzed image. >

Model-based orientation-independent 3-D machine vision techniques

Abstract: Orientation-dependent techniques for the identification of a three-dimensional (3-D) object by a machine vision system are represented in parts. In the first part, the data consist of intensity images of polyhedral objects obtained by a single camera, while in the second part, the data consist of range images of curved objects obtained by a laser scanner. In both cases, the attributed graph representation of the 3-D object surface is used to drive the respective algorithm. In this representation, a graph node represents a surface path and a link, the adjacency between two patches. The attributes assigned to nodes are moment invariants of the corresponding face for polyhedral objects. For range images, the Gaussian curvature is used as a segmentation criterion for providing symbolic shape attributes. Identification is achieved by an efficient graph-matching algorithm used to match the graph obtained from the data to a subgraph of one of the model graphs stored in the computer memory. >

A general index mapping technique for array reconfiguration

Abstract: The reconfiguration of rectangular arrays is considered from a novel, totally general point of view (that can be immediately extended to an array connectivity besides the rectangular one). The only constraint specifically taken into account is that of interconnection locality, represented through the adjacency domain of any given cell in the array; reconfiguration is described as index-mapping. A coverage table is used to represent such index mapping: it is seen that its solution coincides with that of a complete matching problem, and existing algorithms to this purpose are analyzed to identify the best-suited ones. Complexity bounds for the interconnection networks supporting reconfiguration are then determined, and they are seen to be dependent only on the adjacency domain chosen, not on the dimensions of the array. The results are pertinent to the problem of the fault tolerance of VLSI and WSI arrays. >

Voronoi and Related Neighbors on Digitized two-Dimensional Space with Applications to Texture Analysis

Abstract: In this article, we present neighbor relations among figures on a 2-D digitized picture. First those relations (the Voronoi neighbor, the relative neighbor, and the Gabriel neighbor) are extended to a set of connected components (arbitrary shapes of figures). Second, several procedures to obtain those neighbor relations from a given binary image are described with estimation of the amount of computation required. Finally applications of the adjacency graphs induced from the above neighbor relations to texture analysis are described with the results of experiments.

Threaded linear hierarchical quadtrees for computation of geometric properties of binary images

Abstract: A modification of the linear quadtree, the threaded linear hierarchical quadtree (TLHQT), is proposed for the computation of geometric properties of binary images. Since most of the algorithms used in connection with computation of geometric properties require frequent exploration of adjacencies, a structure that keeps permanently in memory some adjacency links is introduced. Some results obtained by using the TLHQT for labeling connected components and for evaluating the perimeter and Euler's number in a quadtree environment are presented. The performance of the TLHQT is discussed. >

Transitive Closure Algorithms for Very Large Databases

Abstract: Nontraditional applications of database systems require the efficient evaluation of recursive queries. The transitive closure of a binary relation has been identified as an important and frequently occurring special case. Traditional algorithms for computing the transitive closure, as developed in the field of algorithmic graph theory, hold both the operand relation and the result relation within directly addressable main memory. The newly anticipated applications, however, deal with very large relations that do not fit into main memory and therefore must be blockwise paged to and from secondary storage. Thus we have to design algorithms and optimization methods for computing the transitive closure of very large relations. We survey and compare various such algorithms and methods in a unifying manner. In particular we identify eight basic strategies to generate and to refine transitive closure algorithms: algebraic manipulation, implementation of the join operator, reusage of newly generated tuples, enforcement of some ordering of tuples, blocking of adjacency lists, tuning and preprocessing, taking advantage of topological order, and selection of an access structure for adjacency lists. The analysis demonstrates the great variety of options on the different description levels and how they are compatible. Based on experiments some specific algorithms are recommended.

Eigenvectors of distance-regular graphs

Abstract: The objective of this work is to find properties of a distance-regular graph G that are expressed in the eigenvectors of its adjacency matrix. The approach is to consider the rows of a matrix of orthogonal eigencolumns as (coordinates of) points in Euclidean space, each one corresponding to a vertex of G. For the second eigenvalue, the symmetry group of the points is isomorphic to the automorphism group of G. Adjacency of vertices is related to linear dependence, linear independence, and proximity of points. Relative position of points is studied by way of the polytope that is their convex hull. Several families of examples are included.

The automorphism group of random graphs with a given number of edges

Abstract: An automorphism σ(G) of a graph G is a permutation of the set of its vertices which preserves adjacency. Under the operation of composition the automorphisms of G form a group Aut(G). The graph G is called asymmetric if Aut(G) is trivial, and symmetric otherwise.

PLEXUS: A System for Implementing Hierarchical Graph Algorithms

Abstract: The PLEXUS system has been developed for the support of the implementation of hierarchical graph algorithms. Such algorithms process hierarchically defined graphs as described in [LeWa 87a] or cellular graph grammars as described in [LeWa 87b]. In these references the folded parse tree of the hierarchically defined graph resp. the folded parse trees of the graphs in a cellular graph language are processed bottom-up in order to solve a graph problem. In each step the graph corresponding to a subtree of the parse tree is exchanged with a small replaceable graph. The replaceable graph is created by a so-called burning procedure, such that it does not alter the graph property under investigation (see [LeWa 87a, LeWa 87b]). PLEXUS supports the implementation of hierarchical graph algorithms based on the bottomup method by providing the necessary basic data structures and functions. The system is organized in several layers which are described in detail in the following :

Learning by Choice of Internal Representations

Abstract: We introduce a learning algorithm for multilayer neural networks composed of binary linear threshold elements. Whereas existing algorithms reduce the learning process to minimizing a cost function over the weights, our method treats the internal representations as the fundamental entities to be determined. Once a correct set of internal representations is arrived at, the weights are found by the local and biologically plausible Perceptron Learning Rule (PLR). We tested our learning algorithm on four problems: adjacency, symmetry, parity and combined symmetry-parity.

Architectural solutions for intermediate-level vision

Abstract: A difficult problem for designers of real-time machine vision systems is handling the iconic/symbolic interface. While image-to-image transformations are readily computed by both pipelined and image-parallel architectures, and list-based and logic-based processors handle symbolic information efficiently, there has all too often been a bottleneck in handling the conversion of iconic data into symbolic form and vice-versa. There is a wide variety of operations that convert images into scalars, contour lists, or other non-iconic descriptions; however, these operations are relatively inefficient on most commercial and research systems.

Hierarchical structure to winged-edge structure: a conversion algorithm

Abstract: The winged-edge data structure is advantageous for traversing the topological graph of the boundary representation of a solid object. This paper presents an algorithm for converting hierarchical boundary representations into representations in the winged-edge data structure. As a result of the conversion, the adjacency relationships of geometric entities embedded in hierarchical boundary representations,-which may be evaluated through boundary evaluation on solid objects defined via Boolean set-operations, can be easily and efficiently accessed.

Semiregular graphs and their algebra

Abstract: A semiregular graph is a bipartite graph which, from the point of view of the vertices of one of the partite sets, appears to be distance regular. Many facts about distance-regular graphs remain true for this class: the adjacency matrix has d + 1 eigenvalues (d=diameter); the eigenmatnx associated with the second eigenvalue can provide a representation of the automorphism group; the coloration matrix represents the adjacency matrix in the span of the "distance matrices", and its eigenvectors provide eigenvectors of the adjacency matrix.

A procedural approach to view independent three-dimensional object recognition and pose determination

Abstract: The purpose of this research was to develop a robust paradigm for the model matching phase of a view independent object recognition system. The approach taken in this thesis represents both the image and the model conceptually as a graph structure. The model graph, however, is implemented as a procedure, and is therefore referred to as a Procedural Model. Binary relations between nodes in the object graph are implemented implicitly by the calling relations between procedures. A collection of such procedures and the calling relations between them provides a full depth-first search of the tree of possible model node to image node bindings. A complete image analysis system was developed and used to demonstrate the functionality and usefulness of the Procedural Model approach to object recognition. Although arbitrarily complex search trees can be implemented in this way, the syntax of the individual model procedures is shown to be so similar, for objects composed of analytic surfaces, that such models can be built automatically. An interactive program has been written which can be used to construct a Procedural Model by prompting only for object-specific information. A new more general definition of an aspect is presented and used to extend the concept of stable states. These two ideas together form a basis of the Procedural Model approach to view independent object recognition. The concept of the region adjacency graph was also extended by assigning a priority to the patches in the graph, and by including three-dimensional information. Once the presence of an object is detected and that object identified, its pose is computed.

A machine vision identification technique from range images

Abstract: An orientation-independent identification technique from three-dimensional surface maps or range images is developed. Given the range image of an object, it is decomposed into orientation-independent patches using the sign of Gaussian curvature. A relational graph is then set up such that a node represents a patch and an edge represents the adjacency of two patches. The identification of the object is achieved by matching its graph representation to a number of model graphs. The matching is performed by employing the best-first search strategy. Examples of real range images show the merit of the technique.

'Double' subgraph isomorphism method for matching LSI chip images

Abstract: The corresponding relations between two nodes isomorphically matched are searched from the region adjacency graph of segmented chip images. Heuristic information is extracted to improve the searching efficiency in the isomorphism matching. Special criteria of region similarity measure and matching figure of surrounding string are used to select starting nodes of isomorphism matching. >

Adjacency Finding Algorithms in a Variable-Resolution Boundary Model

Abstract: A variable-resolution boundary model of three dimensional objects provides a representation of the surfaces enclosing it at successively finer levels of specification. A hierarchical graph structure, called a structured edge-face graph (SEFG) is described, which encodes the boundary of a solid object at variable resolution is described. The structured edge-face graph is based on a face-oriented relational description of the object boundary. The concept of adjacency relation between pairs of primitive boundary entities at fixed accuracy is introduced, and adjacency finding algorithms which operate on a structured edge-face graph object representation are presented.