Indexing and querying color sets of images

摘要

We aim to study the set of color sets of continuous regions of an image given as a matrix of m rows over n >= m columns where each element in the matrix is an integer from [1, sigma] named a 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 F. A rectangle is 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 L. We first explain how to determine all the vertical bar L vertical bar maximal locations with their fingerprints in expected time O (nm(2)sigma) using a Monte Carlo algorithm (with polynomially small probability of error) or within deterministic O (nm(2)sigma log(vertical bar L vertical barm(2) + 2)) time. We then show how to build a data structure which occupies O(nm logn + vertical bar L vertical bar) space such that a query which asks for all the maximal locations with a given fingerprint f can be answered in time O(vertical bar f vertical bar + log logn + 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 (nm logn + vertical bar F vertical bar) while the query time becomes O(nm log logn + vertical bar F vertical bar). We eventually consider the special case of squared regions (squares). (C) 2016 Elsevier B.V. All rights reserved.