![]() ![]() The similarity of the mathematical expression for the numerator of the NCC (see section 1, Eq (4)) with that of a convolution is striking and implicates that its computation must be optimal in the Fourier transform space. ![]() NCC is one of those quantities with application in a variety of research fields as diverse as physics, signal processing, engineering, medical imaging, and statistical finance. The simplest form of the normalized cross-correlation (NCC) is the cosine of the angle θ between two vectors a and b: ![]() This dependency is eliminated if one uses the normalized form of the covariance, referred to as the normalized cross-correlation (otherwise known as the correlation coefficient). A serious setback of the covariance is its dependence on the amplitude of either of the series that are compared. Covariance, by definition, provides a measure of the strength of the correlation between two sets of numbers (or time series). ![]()
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