An algorithm for identifying symmetry of a 3-D 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.>

Describes a technique for symmetry detection and measurement of 3D medical entities based on an algorithm for general 3D symmetry identification. The technique can recognize a number of symmetries including bilateral, central, and rotational; and it expresses them in terms of a symmetry measure called 'the symmetry degree'. It is based on traversals of the octree obtained by the principal axis transform of the input octree, therefore it requires that the medical entity be represented by its octree. This may be the only technique for 3D symmetry measurement that can deal with arbitrary medical entities. The procedure is demonstrated on two skull models reconstructed from axial CT scans but it is applicable to entity models obtained by other techniques as well. It is also shown how to use this procedure for invariant alignment of different images of the same entity for their comparative analysis.>