Homotopy based Surface Reconstruction with Application to Acoustic Signals

Ojaswa Sharma, François Anton

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    This work introduces a new algorithm for surface reconstruction in a"e(3) from spatially arranged one-dimensional cross sections embedded in a"e(3). This is generally the case with acoustic signals that pierce an object non-destructively. Continuous deformations (homotopies) that smoothly reconstruct information between any pair of successive cross sections are derived. The zero level set of the resulting homotopy field generates the desired surface. Four types of homotopies are suggested that are well suited to generate a smooth surface. We also provide derivation of necessary higher order homotopies that can generate a C (2) surface. An algorithm to generate surface from acoustic sonar signals is presented with results. Reconstruction accuracies of the homotopies are compared by means of simulations performed on basic geometric primitives.
    Original languageEnglish
    JournalVisual Computer
    Volume27
    Issue number5
    Pages (from-to)373-386
    ISSN0178-2789
    DOIs
    Publication statusPublished - 2011

    Keywords

    • Sonar
    • Surface reconstruction
    • Homtopy
    • Continuous deformations

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