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    Near-Regular Structure Discovery Using Linear Programming

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    Type
    Article
    Authors
    Huang, Qixing
    Guibas, Leonidas J.
    Mitra, Niloy J. cc
    Date
    2014-06-02
    Permanent link to this record
    http://hdl.handle.net/10754/598961
    
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    Abstract
    Near-regular structures are common in manmade and natural objects. Algorithmic detection of such regularity greatly facilitates our understanding of shape structures, leads to compact encoding of input geometries, and enables efficient generation and manipulation of complex patterns on both acquired and synthesized objects. Such regularity manifests itself both in the repetition of certain geometric elements, as well as in the structured arrangement of the elements. We cast the regularity detection problem as an optimization and efficiently solve it using linear programming techniques. Our optimization has a discrete aspect, that is, the connectivity relationships among the elements, as well as a continuous aspect, namely the locations of the elements of interest. Both these aspects are captured by our near-regular structure extraction framework, which alternates between discrete and continuous optimizations. We demonstrate the effectiveness of our framework on a variety of problems including near-regular structure extraction, structure-preserving pattern manipulation, and markerless correspondence detection. Robustness results with respect to geometric and topological noise are presented on synthesized, real-world, and also benchmark datasets. © 2014 ACM.
    Citation
    Huang Q, Guibas LJ, Mitra NJ (2014) Near-Regular Structure Discovery Using Linear Programming. ACM Transactions on Graphics 33: 1–17. Available: http://dx.doi.org/10.1145/2535596.
    Sponsors
    This work was supported by NSF grant CCF-1011228, Marie Curie Career Integration Grant 303541, ERC Starting Grant SmartGeometry 335373, a KAUST-Stanford AEA grant, a KAUST visiting scholarship, a Google research award, and a Stanford Graduate Fellowship.
    Publisher
    Association for Computing Machinery (ACM)
    Journal
    ACM Transactions on Graphics
    DOI
    10.1145/2535596
    ae974a485f413a2113503eed53cd6c53
    10.1145/2535596
    Scopus Count
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    Publications Acknowledging KAUST Support

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