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P. Minovic, S. Ishikawa, K. Kato, "Symmetry Identification of a 3D Object Represented by Octree," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 15, no. 5, pp. 507514, May, 1993.  
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@article{ 10.1109/34.211472, author = {P. Minovic and S. Ishikawa and K. Kato}, title = {Symmetry Identification of a 3D Object Represented by Octree}, journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence}, volume = {15}, number = {5}, issn = {01628828}, year = {1993}, pages = {507514}, doi = {http://doi.ieeecomputersociety.org/10.1109/34.211472}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Pattern Analysis and Machine Intelligence TI  Symmetry Identification of a 3D Object Represented by Octree IS  5 SN  01628828 SP507 EP514 EPD  507514 A1  P. Minovic, A1  S. Ishikawa, A1  K. Kato, PY  1993 KW  3D object recognition; image recognition; symmetry identification; octree; principal axis transform; complexity; image recognition; trees (mathematics) VL  15 JA  IEEE Transactions on Pattern Analysis and Machine Intelligence ER   
An algorithm for identifying symmetry of a 3D object given by its octree is presented, and the symmetry degree (a measure of object symmetry) is proposed. The algorithm is based on traversals of the octree obtained by the principal axis transform of an input octree. An object can be in an arbitrary position and with arbitrary orientation within the octree space, and a wide range of symmetries represented by groups of proper and improper rotations can be identified. It is shown that the octree data structure supports these operations well, especially for objects whose symmetry types are simpler or equal in complexity with a fourfold rotational symmetry. The operation of the algorithm is illustrated using some synthetic test objects. The results, which are composed of identified symmetry types and the corresponding symmetry degrees, were satisfactory.
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