Homotopic Object Reconstruction Using Natural Neighbor Barycentric Coordinates

Ojaswa Sharma, François Anton

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    Abstract

    One of the challenging problems in computer vision is object reconstruction from cross sections. In this paper, we address the problem of 2D object reconstruction from arbitrary linear cross sections. This problem has not been much discussed in the literature, but holds great importance since it lifts the requirement of order within the cross sections in a reconstruction problem, consequently making the reconstruction problem harder. Our approach to the reconstruction is via continuous deformations of line intersections in the plane. We define Voronoi diagram based barycentric coordinates on the edges of n-sided convex polygons as the area stolen by any point inside a polygon from the Voronoi regions of each open oriented line segment bounding the polygon. These allow us to formulate homotopies on edges of the polygons from which the underlying object can be reconstructed. We provide results of the reconstruction including the necessary derivation of the gradient at polygon edges.
    Original languageEnglish
    Title of host publicationSeventh International Symposium on Voronoi Diagrams in Science and Engineering : ISVD 2010
    PublisherIEEE
    Publication date2010
    ISBN (Print)978-1-4244-7606-0
    DOIs
    Publication statusPublished - 2010
    Event7th International Symposium on Voronoi Diagrams in Science and Engineering - Quebec city, Canada
    Duration: 28 Jun 201030 Jun 2010
    Conference number: 7
    http://isvd2010.scg.ulaval.ca/

    Conference

    Conference7th International Symposium on Voronoi Diagrams in Science and Engineering
    Number7
    CountryCanada
    CityQuebec city
    Period28/06/201030/06/2010
    Internet address

    Keywords

    • Reconstruction
    • Linear cross sections
    • Continuous deformations
    • Homotopy

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