These aren't exactly 0, due to random sampling. set.seed(101)ĭefine a function to do the cosine similarity (no demeaning), and compare against the Pearson correlation ( cor() function): cossim <-function(x,y) sum(x*y)/sqrt(sum(x^2)*sum(y^2)) To illustrate with a simple example, generate two (ideally) uncorrelated vectors from a standard normal distribution (mean 0, standard deviation 1) in R.
The advantage of demeaning is removing influence from overall levels. So the normalized cross-correlation that you show is related to a Pearson correlation, while your proposal is related to a more general cosine similarity. This is similar to the difference between Pearson correlation and cosine similarity.Īs explained here for example, the Pearson correlation is the cosine similarity between two demeaned vectors. The cross-correlation of the image and the feature at $u,v$ is denoted by $c(u,v)$ and defined as $$ c(u,v) = \sum_$$ I'm following Lewis (1995) exposition on normalized cross correlation for template matching (Section 2).
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