Multi-Scale Partial Intrinsic Symmetry Detection

ACM Transactions on Graphics(Proceedings of SIGGRAPH ASIA 2012)

Kai Xu 1,2     Hao Zhang3      Wei Jiang1     Ramsay Dyer4     Zhiquan Cheng1     Ligang Liu5     Baoquan Chen2    

1National University of Defense Technology
2Shenzhen VisuCA Key Lab/SIAT
3Simon Fraser University
5University of Science and Technology of China

Figure 1:   Multi-scale partial intrinsic symmetry detection: five symmetry scales (large to small) are detected. Each symmetric region is shown in uniform color. Note the detection of inter- and intra-object symmetries, as well as cylindrical symmetry of the limbs.



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.





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We would first like to thank the anonymous reviewers for their valuable feedback. Thanks also go to Daniel Cohen-Or for fruitful discussions on the paper. Part of the 3D models in this paper is from the shape repositories of AIM@SHAPE and Stanford. This work is supported in part by grants from NSFC (61202333, 61232011, 61161160567, 61025012, 61103084, and 61070071), NSERC (No. 611370), National 863 Program (2011AA010503), Shenzhen Science and Innovation Program (CXB201104220029A, JC201005270329A), the 973 National Basic Research Program of China (2011CB302400).


@ARTICLE{Active 2012,
  title = {Multi-Scale Partial Intrinsic Symmetry Detection},
  author = {Kai Xu and Hao Zhang and Wei Jiang and Ramsay Dyer and Zhiquan Cheng and Ligang Liu and Baoquan},
  journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH ASIA 2012)},
  volume = { },
  issue = {4},
  pages = { },
  year = 2012