Ranklets a Complete Family of Multiscale, Orientation Selective Rank Features

Smeraldi, Research Report RR0309-01, Department of Computer Science, Queen Mary, University of London, Mile End Road, London E1 4NS, UK, September 2003

Abstract

Ranklets are a family of non-parametric rank features designed in close analogy with Haar wavelets. With these they share the same pattern of orientation selectivity, the multiscale nature and a suitable notion of completeness. Ranklets are defined based on the Wilcoxon statistics, are computationally efficient and admit an interpretation in terms of pairwise pixel comparisons. In this report we review the definition of ranklets and their geometric properties. We then introduce a notion of completeness applicable to rank features and give proofs for one and two dimensional ranklets. Finally, we present a few considerations on the algorithmic complexity of the representation and its memory efficiency.

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