3107205
Crossing Minimization for Symmetries
AbstractWe consider the problem of drawing a graph with a given symmetry
 such that the number of edge crossings is minimal. We show that this
 problem is NP-hard, even if the order of orbits around the rotation
 center or along the reflection axis is fixed.
 We devise an O(m log m) algorithm
 for computing a crossing minimal drawing if inter-orbit edges may
 not cross orbits, showing in particular that intra-orbit edges do
 not contribute to the NP-hardness of the crossing minimization
 problem for symmetries.
9291771
Drawing Trees Symmetrically in Three Dimensions
AbstractSymmetric graph drawing enables a clear understanding of the structure of the graph. Previous work on symmetric graph drawing has focused on two dimensions. Symmetry in three dimensions is much richer than that of two dimensions. This is the first paper to extend symmetric graph drawing into three dimensions. More specifically, the paper investigates the problem of drawing trees symmetrically in three dimensions. First, we suggest a model for drawing trees symmetrically in three dimensions. Based on this model, we present a linear time algorithm for finding the maximum number of three-dimensional symmetries in trees. We also present a three-dimensional symmetric drawing algorithm for trees.

10549206
Regular graph coverings whose covering transformation groups have the isomorphism extension property
Abstract Enumerative results are presently a major center of interest in topological graph theory, as in the work of Gross and Furst [1], Hofmeister [5,6], Kwak and Lee [9–13] and Mull et al. [15], etc. Kwak and Lee [9] enumerated the isomorphism classes of graph bundles and those of n -fold graph coverings with respect to a group of automorphisms of the base graph which fix a spanning tree. Hofmeister [6] enumerated independently the isomorphism classes of n -fold graph coverings with respect to the trivial automorphism group of the base graph. But the enumeration of isomorphism classes of regular graph coverings has not been answered completely. As its partial answers, Hofmeister enumerated the isomorphism classes of Z 2 -coverings (double coverings) with respect to any group of automorphisms of the base graph, and Sato [14] did the same work for Z p -coverings (regular prime-fold coverings). With respect to the trivial automorphism group of the base graph, Hong and Kwak [8] did the same work for Z 2 ⊕ Z 2 or Z 4 -coverings, and Kwak and Lee [10] did it for Z p , Z p ⊕ Z 1 ( p ≠ q primes) or Z p 2 -coverings. As an expansion of this effort, we obtain in this paper several new algebraic characterizations for isomorphic regular coverings and derive an enumerating formula for the isomorphism classes of A-coverings of a graph G with respect to any group of automorphisms of G which fix a spanning tree, when the covering transformation group A has the isomorphism extension property. By definition, it means that every isomorphism between any two isomorphic subgroups B 1 and B 2 of A can be extended to an automorphism of A. Also, we obtain complete numerical enumeration of the isomorphism classes of Z n -coverings for all n , D n -coverings for odd n (D n is the dihedral group of order 2 n ) or Z p ⊕ Z p -coverings of a graph G for prime p with respect to the trivial automorphism group of G . In addition, we applied our results to a bouquet of circles.
653040
The Puzzle Layout Problem
This poster describes an implementation of the puzzle generators and puzzle layouts introduced in [1].
1395152
A Group-Theoretic Method for Drawing Graphs Symmetrically
Constructing symmetric drawings of graphs is NP-hard. In this paper, we present a new method for drawing graphs symmetrically based on group theory. More formally, we define a n-geometric automorphism group of a graph that can be displayed as symmetries of a drawing of the graph in n dimensions. Then we present an algorithm to find all 2- and 3-geometric automorphism groups of a graph. We implement the algorithm using Magma [11] and the experimental results shows that our approach is very efficient in practice. We also present a drawing algorithm to display a 2- or 3-geometric automorphism group.
1910054
A neuromorphic model for achromatic and chromatic surface representation of natural images
This study develops a neuromorphic model of human lightness perception that is inspired by how the mammalian visual system is designed for this function. It is known that biological visual representations can adapt to a billion-fold change in luminance. How such a system determines absolute lightness under varying illumination conditions to generate a consistent interpretation of surface lightness remains an unsolved problem. Such a process, called 'anchoring' of lightness, has properties including articulation, insulation, configuration, and area effects. The model quantitatively simulates such psychophysical lightness data, as well as other data such as discounting the illuminant, and lightness constancy and contrast effects. The model retina embodies gain control at retinal photoreceptors, and spatial contrast adaptation at the negative feedback circuit between mechanisms that model the inner segment of photoreceptors and interacting horizontal cells. The model can thereby adjust its sensitivity to input intensities ranging from dim moonlight to dazzling sunlight. A new anchoring mechanism, called the Blurred-Highest-Luminance-As-White rule, helps simulate how surface lightness becomes sensitive to the spatial scale of objects in a scene. The model is also able to process natural color images under variable lighting conditions, and is compared with the popular RETINEX model.
20165974
An intelligent image retrieval system using XML
With the rapid development of Internet technology, the number of Internet users and the amount of multimedia information on the Internet is ever increasing. Recently, the Web sites, such as e-business sites and shopping mall sites, deal with lots of image information. As a result, it is required to support content-based image retrieval efficiently on such image data. This paper proposes an intelligent image retrieval system, which adopts XML technology. To support object-based content retrieval on product catalog images containing multiple objects, we describe a multilevel metadata structure representing the local features, global features, and semantics of image data. To enable semantic-based and content-based retrieval on such image data, we design an XML-schema for the proposed metadata. We also describe how to automatically transform the retrieval results into the forms suitable for the various user environments, such as Web browser or mobile browser, using XSLT. The proposed scheme can be utilized to enable efficient image metadata sharing between systems, and it will contribute in improving the retrieval correctness and the user's satisfaction on content-based e-catalog image retrieval.