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What does $N.\hat{N}_{fa}(S)$ mean, when $\hat{N}_{fa}(S)$ is a cumulative distribution function? $\hat{N}_{fa}(S) = \sum\limits_{s=0}^{S}\hat{p}_{fa}(s)$

The formula is from this paper (section 4.2): Logo Retrieval with A Contrario Visual Query Expansion

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    Sure, see my edit.2011-02-10

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I'm pretty sure $N$ in the context means the size of the set $\Omega$, the total number of images. See beginning of section 3.1 of the linked paper. And in $N.\hat{N}_{fa}(S)$, the $.$ should just be multiplication. So the entire term should be interpreted as a distribution of the number of false alarms (total number times the cumulative distribution).

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    @tauran: good and bad formatting is partly subjective (although there are of course guides like the _Chicago Manual of Style_); that said, I feel that you are quite justified in feeling that way.2011-02-10