Symmetry factored embedding and distance
ACM SIGGRAPH 2010 papers
3-D Symmetry Detection and Analysis Using the Pseudo-polar Fourier Transform
International Journal of Computer Vision
Unsupervised Learning for Graph Matching
International Journal of Computer Vision
Tensor based sparse decomposition of 3D shape for visual detection of mirror symmetry
Computer Methods and Programs in Biomedicine
Adaptive unsupervised multi-view feature selection for visual concept recognition
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part I
Diffusion pruning for rapidly and robustly selecting global correspondences using local isometry
ACM Transactions on Graphics (TOG)
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We present a spectral approach for detecting and analyzing rotational and reflectional symmetries in n-dimensions. Our main contribution is the derivation of a symmetry detection and analysis scheme for sets of points in {{\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}}^{n} and its extension to image analysis by way of local features. Each object is represented by a set of points S\in {{\hbox{\rlap{I}\kern 2.0pt{\hbox{R}}}}}^{n}, where the symmetry is manifested by the multiple self-alignments of S. The alignment problem is formulated as a quadratic binary optimization problem, with an efficient solution via spectral relaxation. For symmetric objects, this results in a multiplicity of eigenvalues whose corresponding eigenvectors allow the detection and analysis of both types of symmetry. We improve the scheme's robustness by incorporating geometrical constraints into the spectral analysis. Our approach is experimentally verified by applying it to 2D and 3D synthetic objects as well as real images.