Topic
Adjacency list
About: Adjacency list is a research topic. Over the lifetime, 4419 publications have been published within this topic receiving 78449 citations.
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30 Jun 2003
TL;DR: The utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects is illustrated.
Abstract: In this paper we explore how to use spectral methods for embedding and clustering unweighted graphs. We use the leading eigenvectors of the graph adjacency matrix to define eigenmodes of the adjacency matrix. For each eigenmode, we compute vectors of spectral properties. These include the eigenmode perimeter, eigenmode volume, Cheeger number, inter-mode adjacency matrices and intermode edge-distance. We embed these vectors in a pattern-space using two contrasting approaches. The first of these involves performing principal or independent components analysis on the covariance matrix for the spectral pattern vectors. The second approach involves performing multidimensional scaling on the L2 norm for pairs of pattern vectors. We illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects.
20 citations
12 May 2004
TL;DR: The Similarity Flooding approach and Hopfield-style neural networks are adapted from the graph matching community to the needs of HARAG comparison showing the framework's general applicability to content-based image retrieval of medical images.
Abstract: Content-based image retrieval requires a formal description of visual information. In medical applications, all relevant biological objects have to be represented by this description. Although color as the primary feature has proven successful in publicly available retrieval systems of general purpose, this description is not applicable to most medical images. Additionally, it has been shown that global features characterizing the whole image do not lead to acceptable results in the medical context or that they are only suitable for specific applications. For a general purpose content-based comparison of medical images, local, i.e. regional features that are collected on multiple scales must be used. A hierarchical attributed region adjacency graph (HARAG) provides such a representation and transfers image comparison to graph matching. However, building a HARAG from an image requires a restriction in size to be computationally feasible while at the same time all visually plausible information must be preserved. For this purpose, mechanisms for the reduction of the graph size are presented. Even with a reduced graph, the problem of graph matching remains NP-complete. In this paper, the Similarity Flooding approach and Hopfield-style neural networks are adapted from the graph matching community to the needs of HARAG comparison. Based on synthetic image material build from simple geometric objects, all visually similar regions were matched accordingly showing the framework's general applicability to content-based image retrieval of medical images.
20 citations
TL;DR: A content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters is defined and completely solved.
Abstract: We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.
20 citations
TL;DR: If M is 4-connected, elements e, f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph and a theorem about disjoint paths in graphs is deduced.
Abstract: We say that two elements e , f of a binary matroid M are ‘adjacent’ if there is no minor of M isomorphic to ℳ( K 4 ) which uses both e and f and in which they correspond to opposite edges. We give a good characterization of when two elements are adjacent. In particular, we show that if M is 4-connected, elements e , f are adjacent if and only if M is either graphic or cographic and the elements correspond to adjacent edges of the graph. We deduce a theorem about disjoint paths in graphs.
20 citations
01 Dec 2007
TL;DR: The method presented overcomes a primary bottleneck associated with this approach, which is determining cell adjacency, by employing a technique found in Geographic Information Systems known as tesseral addressing.
Abstract: This paper describes a complete implementation of the Approximate Cell Decomposition approach to path planning. The method presented overcomes a primary bottleneck associated with this approach, which is determining cell adjacency. This increased efficiency is achieved by employing a technique found in Geographic Information Systems known as tesseral addressing.
20 citations