Discovering structural regularity in 3D geometry
Abstract
We introduce a computational framework for discovering regular or repeated geometric structures in 3D shapes. We describe and classify possible regular structures and present an effective algorithm for detecting such repeated geometric patterns in point- or meshbased models. Our method assumes no prior knowledge of the geometry or spatial location of the individual elements that define the pattern. Structure discovery is made possible by a careful analysis of pairwise similarity transformations that reveals prominent lattice structures in a suitable model of transformation space. We introduce an optimization method for detecting such uniform grids specifically designed to deal with outliers and missing elements. This yields a robust algorithm that successfully discovers complex regular structures amidst clutter, noise, and missing geometry. The accuracy of the extracted generating transformations is further improved using a novel simultaneous registration method in the spatial domain. We demonstrate the effectiveness of our algorithm on a variety of examples and show applications to compression, model repair, and geometry synthesis.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Aug 01, 2008
- Source ID
- 10.1145/1360612.1360642
Entities
People
- Helmut Pottmann
- Johannes Wallner
- Leonidas J. Guibas
- Mark Pauly
- Niloy J. Mitra
Organizations
- Defense Advanced Research Projects Agency
- ETH Zurich
- Graz University of Technology
- Indian Institute of Technology Delhi
- National Institutes of Health
- National Science Foundation
- National Science Foundation Division of Mathematical Sciences
- Stanford University
- TU Wien