The quadratic-chi histogram distance family

Ofir Pele*, Michael Werman

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

188 Scopus citations


We present a new histogram distance family, the Quadratic-Chi (QC). QC members are Quadratic-Form distances with a cross-bin χ2-like normalization. The cross-bin χ2-like normalization reduces the effect of large bins having undo influence. Normalization was shown to be helpful in many cases, where the χ2 histogram distance outperformed the L2 norm. However, χ2 is sensitive to quantization effects, such as caused by light changes, shape deformations etc. The Quadratic-Form part of QC members takes care of cross-bin relationships (e.g. red and orange), alleviating the quantization problem. We present two new cross-bin histogram distance properties: Similarity-Matrix-Quantization- Invariance and Sparseness-Invariance and show that QC distances have these properties. We also show that experimentally they boost performance. QC distances computation time complexity is linear in the number of non-zero entries in the bin-similarity matrix and histograms and it can easily be parallelized. We present results for image retrieval using the Scale Invariant Feature Transform (SIFT) and color image descriptors. In addition, we present results for shape classification using Shape Context (SC) and Inner Distance Shape Context (IDSC). We show that the new QC members outperform state of the art distances for these tasks, while having a short running time. The experimental results show that both the cross-bin property and the normalization are important.

Original languageAmerican English
Title of host publicationComputer Vision, ECCV 2010 - 11th European Conference on Computer Vision, Proceedings
PublisherSpringer Verlag
Number of pages14
EditionPART 2
ISBN (Print)3642155510, 9783642155512
StatePublished - 2010
Event11th European Conference on Computer Vision, ECCV 2010 - Heraklion, Crete, Greece
Duration: 10 Sep 201011 Sep 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 2
Volume6312 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference11th European Conference on Computer Vision, ECCV 2010
CityHeraklion, Crete


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