Three-Dimensional Symmetry Identification Part I : Theory
Predrag Minovic, Seiji Ishikawa, Kiyoshi Katō · Institutional Repositories DataBase (IRDB) · 1992
A theoretical background necessary for symmetry identification of an arbitrary, finite, threedimensional object at any position and with arbitrary orientation'is presented.It supports construction of an algorithm for identification of a wide range of symmetry types represented by groups of proper and improper rotations and location of corresponding axes and/or planes of symmetry.The prerequisite is that the input object be represented by an octree.The proposed technique is based on examination of the octree obtained by the principal axis transform of the input octree.It is shown that the octree data structure is very convenient for symmetry evaluation, especially for objects whose symmetry types are simpler or equal in complexity with the four-fold rotational symmetry.The cases when the principal axis transform is not uniquely defined are analyzed and possible solutions are offered.Finally, extensions to multidimensional gray-scale images are briefly discussed.