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The application of a normalized correlation function in image analysis
Author(s) -
Vollath D.
Publication year - 1981
Publication title -
journal of microscopy
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.569
H-Index - 111
eISSN - 1365-2818
pISSN - 0022-2720
DOI - 10.1111/j.1365-2818.1981.tb01240.x
Subject(s) - normalization (sociology) , correlation , mathematics , image (mathematics) , noise (video) , digital image correlation , correlation dimension , correlation function (quantum field theory) , algorithm , pattern recognition (psychology) , artificial intelligence , mathematical analysis , computer science , statistics , physics , optics , spectral density , geometry , fractal dimension , sociology , anthropology , fractal
SUMMARY This paper describes the use of normalized correlation functions, such as auto‐ and cross‐correlation functions for the analysis of images. The normalization is introduced to avoid problems of interpretation of the resulting correlation functions caused by the finite dimension of the image used for calculation. Due to a reduction of noise in the correlation function it is possible to detect periodic structures, which are hidden by noise in the original image. Besides the normalization of the correlation functions, a modification of the correlation function by periodic continuation of the image is proposed. This leads in all cases where the structure allows this to a further drastic reduction of noise. Besides the two‐dimensional correlation functions one‐dimensional correlation functions are proposed. It is shown that there are cases where it is difficult to find an adequate interpretation of these one‐dimensional functions.