Multi-scale partial intrinsic symmetry detection
Kai Xu, Hao Zhang, Wei Jiang, Ramsay Dyer, Zhiquan Cheng, Ligang Liu, Baoquan Chen
In ACM Transactions on Graphics, 31(6), November 2012.
Abstract: We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape. Since different point pairs can share a common point, shape regions covered by points in different scale clusters can overlap. We introduce the symmetry scale matrix (SSM), where each entry estimates the likelihood two point pairs belong to symmetries at the same scale. The pair-to-pair symmetry affinity is computed based on a pair signature which encodes scales. We perform spectral clustering using the SSM to obtain the scale clusters. Then for all points belonging to the same scale cluster, we perform the second-level spectral clustering, based on a novel point-to-point symmetry affinity measure, to extract partial symmetries at that scale. We demonstrate our algorithm on complex shapes possessing rich symmetries at multiple scales.
@article{Xu:2012:MPI,
author = {Kai Xu and Hao Zhang and Wei Jiang and Ramsay Dyer and Zhiquan Cheng and Ligang Liu and Baoquan Chen},
title = {Multi-scale partial intrinsic symmetry detection},
journal = {ACM Transactions on Graphics},
volume = {31},
number = {6},
pages = {181:1--181:11},
month = nov,
year = {2012},
}
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