Influence of selection of discrete set of points on calculation of correlation coefficient in processing of image data

A correlation coefficient is a reliable parameter for a comparison of digital images and correlation techniques find applications in various parts of science and engineering. We perform an analysis of the calculation of a correlation coefficient between two functions (images) which are defined in a specified area on a discrete set of points. The influence of the number of points and their distribution in the specified area on the calculation of the correlation coefficient is investigated. Furthermore, some methods of the choice of data points in specified area are described. The results of this analysis were used in a method for evaluation of interferograms, which can be in principle applied for measurements of the shape of optical surfaces, where the correlation coefficient is used as a measure of the similarity of interference patterns.