On the Detection of the Axes of Symmetry of Symmetric and Almost Symmetric Planar Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Application of the Karhunen-Loeve Procedure for the Characterization of Human Faces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Preserving symmetries in the proper orthogonal decomposition
SIAM Journal on Scientific Computing
Comments on "Symmetry as a Continuous Feature"
IEEE Transactions on Pattern Analysis and Machine Intelligence
Matrix computations (3rd ed.)
3D Symmetry Detection Using The Extended Gaussian Image
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Reflective Symmetry Descriptor for 3D Models
Algorithmica
A Symmetry Preserving Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
A symmetry preserving singular value decomposition
A symmetry preserving singular value decomposition
IEEE Transactions on Computers
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The symmetry preserving singular value decomposition (SPSVD) produces the best symmetric (low rank) approximation to a set of data. These symmetric approximations are characterized via an invariance under the action of a symmetry group on the set of data. The symmetry groups of interest consist of all the nonspherical symmetry groups in three dimensions. This set includes the rotational, reflectional, dihedral, and inversion symmetry groups. In order to calculate the best symmetric (low rank) approximation, the symmetry of the data set must be determined. Therefore, matrix representations for each of the nonspherical symmetry groups have been formulated. These new matrix representations lead directly to a novel reweighting iterative method to determine the symmetry of a given data set by solving a series of minimization problems. Once the symmetry of the data set is found, the best symmetric (low rank) approximation in the Frobenius norm and matrix 2-norm can be established by using the SPSVD.