DMCA
Partial and approximate symmetry detection for 3D geometry (2006)
Cached
Download Links
| Venue: | ACM TRANSACTIONS ON GRAPHICS |
| Citations: | 176 - 26 self |
BibTeX
@ARTICLE{Mitra06partialand,
author = {Niloy J. Mitra and Leonidas J. Guibas and Mark Pauly},
title = { Partial and approximate symmetry detection for 3D geometry},
journal = {ACM TRANSACTIONS ON GRAPHICS},
year = {2006},
volume = {25},
pages = {560--568}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
“Symmetry is a complexity-reducing concept [...]; seek it everywhere.” Alan J. Perlis Many natural and man-made objects exhibit significant symmetries or contain repeated substructures. This paper presents a new algorithm that processes geometric models and efficiently discovers and extracts a compact representation of their Euclidean symmetries. These symmetries can be partial, approximate, or both. The method is based on matching simple local shape signatures in pairs and using these matches to accumulate evidence for symmetries in an appropriate transformation space. A clustering stage extracts potential significant symmetries of the object, followed by a verification step. Based on a statistical sampling analysis, we provide theoretical guarantees on the success rate of our algorithm. The extracted symmetry graph representation captures important highlevel information about the structure of a geometric model which in turn enables a large set of further processing operations, including shape compression, segmentation, consistent editing, symmetrization, indexing for retrieval, etc.
Keyphrases
approximate symmetry detection geometric model simple local shape signature appropriate transformation space statistical sampling analysis man-made object exhibit significant symmetry contain repeated substructure shape compression processing operation complexity-reducing concept verification step potential significant symmetry large set theoretical guarantee important highlevel information euclidean symmetry success rate compact representation consistent editing new algorithm extracted symmetry graph representation clustering stage
