The Role of Optics in Applying Correlation Functions to Pattern Recognition
Dan McLachlan · Journal of the Optical Society of America · 1962
This paper describes some previously invented optical means for performing convolutions (i.e., correlations) of designs in two dimensions and teaches through optics the physical meaning of these functions. The paper also discusses how these operations can be used for pattern recognition and also for measuring the similarity of two patterns. It is shown how the well-known cross-correlations function, A(uv)=1ab∫0a∫0bρ(x,y)ρ′(x+u,y+v)dxdy,is a part of a new function we call here the “similarity” function, S(ρρ′)=1ab∫0a∫0bA2(uv)dudv.This function (having the highest value for identical patterns and lower values for dissimilar patterns) can, like the correlation function, be performed by optical means without any computation whatsoever. The mathematical discussion of the characteristics of S(ρρ′) are given. The possible role of these methods in information retrieval are suggested, and some of the limitations mentioned.