1. Regarding section 9.7.2 Normalized Correlation Metrics In http://orfeo-toolbox.org/SoftwareGuide/SoftwareGuidech9.html#x32-1660009.7
NC is generally defined by the product of the differences to the mean divided by the product of the standard deviations, i.e. see http://en.wikipedia.org/wiki/Cross-correlation In http://orfeo-toolbox.org/SoftwareGuide/SoftwareGuidech9.html#x32-1660009.7 it is stated that NC "computes pixel-wise cross-correlation and normalizes it by the square root of the autocorrelation of the images" and then the formula indicates that what is actually computed in the denominator is sum(A[i]^2), which is *not* equal to autocorr(A[i]) First, the normalization in NC must be by the square root of the product of the variances, not by the autocorrelation. Second, for sum(A[i]^2) to be equal to the variance, you have to previously subtract the mean (aka "centering" in multi-variate statistics terminology) to both A and B. I think this is what is actually being done, but it is not stated. In short: 1.1. The formula is correct, provided the means of A and B have been previously subtracted (but this fact has to be confirmed and explicitly stated). 1.2 The definition is wrong. It should be NC "computes pixel-wise cross-correlation and normalizes it by the square root of the product of the variances of the images". 2. Now, you understand that there is a lot of ambiguity with what is meant by the metrics "cross-correlation (CC) and cross-correlation with subtracted mean (CCSM)" in the Fine Registration page: http://www.orfeo-toolbox.org/Applications/FineRegistration.html 3. Note that the engineering jargon differs from the statistical terminology. In statistics, "Normalized Correlation" is a redundancy, because correlation is always normalized by definition: the NC formula is just the Pearson's coefficient. According to http://en.wikipedia.org/wiki/Cross-correlation, what in engineering is known as CC is what in statistics is called the sum of products of deviation (=numerator of Pearson's coefficient). 4. Therefore, my conjectures are: CC = numerator of Pearson's coefficient NCC = CCSM = Pearson's coefficient Could somebody please confirm or provide the correct answer? Thanks Agus -- -- Check the OTB FAQ at http://www.orfeo-toolbox.org/FAQ.html You received this message because you are subscribed to the Google Groups "otb-users" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/otb-users?hl=en --- You received this message because you are subscribed to the Google Groups "otb-users" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. For more options, visit https://groups.google.com/d/optout.
