Homotopic Object Reconstruction Using Natural Neighbor Barycentric Coordinates

Ojaswa Sharma, François Anton

    Research output: Chapter in Book/Report/Conference proceedingBook chapterResearchpeer-review


    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 and the optimal placement of cutting lines. Accuracy of the suggested reconstruction is evaluated by means of various metrics and compared with one of the existing methods.
    Original languageEnglish
    Title of host publicationTransactions on Computational Science XIV : Special Issue on Voronoi Diagrams and Delaunay Triangulation
    EditorsM. L. Gavrilova
    Publication date2011
    ISBN (Print)978-3-642-25248-8
    ISBN (Electronic)978-3-642-25249-5
    Publication statusPublished - 2011
    Event7th International Symposium on Voronoi Diagrams in Science and Engineering - Quebec city, Canada
    Duration: 28 Jun 201030 Jun 2010
    Conference number: 7


    Conference7th International Symposium on Voronoi Diagrams in Science and Engineering
    CityQuebec city
    Internet address
    SeriesLecture Notes in Computer Science

    Bibliographical note

    Revised and extended version of paper presented at the International Symposium on Voronoi Diagrams 2010. The original paper is published by IEEE: 10.1109/ISVD.2010.19


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