Algorithm to measure symmetry and positional entropy of a data set

摘要

A method and algorithm is given to measure the symmetry (SYM=global symmetry) of N points. The algorithm is based on counting the number of “elementary symmetric recognition acts,” or having two distances d(A,B) and d(C,D) be equal within a given tolerance t. The same algorithm can be adapted to measure un-normalized positional entropy deficit” (UPED) and positional entropy of N point. These parameters (SYM and UPED) represent a “MISSING LINK” connecting symmetry with order/disorder with entropy, since for small occupation numbers (1=k=4) they come out almost the same. Here the occupation number, k, is the number of equal distances in the figure for a given value d. The algorithm can be added via software to imaging devices, such as computer graphic programs or cameras to solve problems of defect detection, say in gems, or object detection.