The Earth Mover's Distance as a Metric for Image Retrieval
International Journal of Computer Vision
Efficient Color Histogram Indexing for Quadratic Form Distance Functions
IEEE Transactions on Pattern Analysis and Machine Intelligence
A fast, non-iterative and exact histogram matching algorithm
Pattern Recognition Letters
Improving similarity measures of histograms using smoothing projections
Pattern Recognition Letters
Efficient matching of large-size histograms
Pattern Recognition Letters
Signatures versus histograms: Definitions, distances and algorithms
Pattern Recognition
A fast and exact modulo-distance between histograms
SSPR'06/SPR'06 Proceedings of the 2006 joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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In this paper we present a new method for comparing histograms. Its main advantage is that it takes less time than previous methods. The present distances between histograms are defined on a structure called signature, which is a lossless representation of histograms. Moreover, the type of the elements of the sets that the histograms represent are ordinal, nominal and modulo. We show that the computational cost of these distances is O(z′) for the ordinal and nominal types and O(z′2) for the modulo one, where z′ is the number of non-empty bins of the histograms. In the literature, the computational cost of the algorithms presented depends on the number of bins in the histograms. In most applications, the histograms are sparse, so considering only the non-empty bins dramatically reduces the time needed for comparison. The distances we present in this paper are experimentally validated on image retrieval and the positioning of mobile robots through image recognition.