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.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.