Assessing distances between pairs of histograms based on relaxed flow constraints
Abstract:
The example embodiments of the invention notably are directed to a computer-implemented method for assessing distances between pairs of histograms. Each of the histograms is a representation of a digital object; said representation comprises bins associating weights to respective vectors. Such vectors represent respective features of said digital object. This method basically revolves around computing distances between pairs of histograms. That is, for each pair {p, q} of histograms p and q of said pairs of histograms, the method computes a distance between p and q of said each pair {p, q}. In more detail, said distance is computed according to a cost of moving p into q, so as to obtain a flow matrix F, whose matrix elements Fi,j indicate, for each pair {i,j} of bins of p and q, how much weight of a bin i of p has to flow to a bin j of q to move p into q. This is achieved by minimizing a quantity Σi,jFi,j·Ci,j, where Ci,j is a matrix element of a cost matrix C representing said cost. Said quantity Σi,jFi,j·Ci,j is minimized under two flow constraints, which, interestingly, include a relaxed flow constraint Fi,j≤ri,j, in addition to a complementary flow constraint. The relaxed flow constraint Fi,j≤ri,j is applied for at least some of the pairs {i,j}, with ri,j equal to pi or qj, where pi and qj are weights associated to bins i and j of p and q, respectively, and the complementary flow constraint is either an out-flow constraint ΣiFi,j=pi if ri,j=qj or an in-flow constraint ΣiFi,j=qj if ri,j=pi. The invention is further directed to related computer program products.
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