Near-Regular Structure Discovery Using Linear Programming
Qixing Huang, Leonidas Guibas, Niloy J. Mitra
ACM Transactions on Graphics 2013


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, i.e., the connectivity relationships among the elements; as well as a continuous aspect, i.e., 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, structurepreserving pattern manipulation, and markerless correspondence detection. Robustness results with respect to geometric and topological noise are presented on synthesized, realworld, and also benchmark datasets.

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We would like to acknowledge the anonymous reviewers for their helpful comments and detailed suggestions, and Henry Adams, Adrian Butscher, Mirela Ben-Chen, Maks Ovsjanikov, and Helmut Pottmann for the extremely useful feedback and discussions. This work was supported by NSF grants 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.


  title = {Near-Regular Structure Discovery Using Linear Programming},
  author = {Qixing Huang and Leonidas Guibas and Niloy J. Mitra},
  journal = {ACM Transactions on Graphics},
  volume = {xx},
  issue = {xx},
  pages = {},
  year = {201x}, 

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