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Register a new userIndexing and querying color sets of images
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Added by
Djamal Belazzougui
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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We aim to study the set of color sets of continuous regions of an image given as a matrix of $m$ rows over $ngeq m$ columns where each element in the matrix is an integer from $[1,sigma]$ named a {em color}. The set of distinct colors in a region is called fingerprint. We aim to compute, index and query the fingerprints of all rectangular regions named rectangles. The set of all such fingerprints is denoted by ${cal F}$. A rectangle is {em maximal} if it is not contained in a greater rectangle with the same fingerprint. The set of all locations of maximal rectangles is denoted by $mathcal{L}.$ We first explain how to determine all the $|mathcal{L}|$ maximal locations with their fingerprints in expected time $O(nm^2sigma)$ using a Monte Carlo algorithm (with polynomially small probability of error) or within deterministic $O(nm^2sigmalog(frac{|mathcal{L}|}{nm^2}+2))$ time. We then show how to build a data structure which occupies $O(nmlog n+mathcal{|L|})$ space such that a query which asks for all the maximal locations with a given fingerprint $f$ can be answered in time $O(|f|+loglog n+k)$, where $k$ is the number of maximal locations with fingerprint $f$. If the query asks only for the presence of the fingerprint, then the space usage becomes $O(nmlog n+|{cal F}|)$ while the query time becomes $O(|f|+loglog n)$. We eventually consider the special case of squared regions (squares).
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