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  • 1
    ISSN: 1432-0541
    Keywords: Triangulation ; Simple polygon ; Visibility ; Shortest paths ; Ray shooting ; Computational geometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of points that are visible from a given segment withinP, preprocessingP for fast "ray shooting" queries, and several related problems.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Algorithmica 1 (1986), S. 49-63 
    ISSN: 1432-0541
    Keywords: Computational geometry ; Computer graphics ; Robotics ; Visibility ; Hidden-line Elimination ; Visibility graph ; Shortest path
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Consider a collection of disjoint polygons in the plane containing a total ofn edges. We show how to build, inO(n 2) time and space, a data structure from which inO(n) time we can compute the visibility polygon of a given point with respect to the polygon collection. As an application of this structure, the visibility graph of the given polygons can be constructed inO(n 2) time and space. This implies that the shortest path that connects two points in the plane and avoids the polygons in our collection can be computed inO(n 2) time, improving earlierO(n 2 logn) results.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    International journal of computer vision 40 (2000), S. 99-121 
    ISSN: 1573-1405
    Keywords: image retrieval ; perceptual metrics ; color ; texture ; Earth Mover's Distance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.
    Type of Medium: Electronic Resource
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