Bin ratio-based histogram distances and their application to image classification

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Large variations in image background may cause partial matching and normalization problems for histogram-based representations, i.e., the histograms of the same category may have bins which are significantly different, and normalization may produce large changes in the differences between corresponding bins. In this paper, we deal with this problem by using the ratios between bin values of histograms, rather than bin values' differences which are used in the traditional histogram distances. We propose a bin ratio-based histogram distance (BRD), which is an intra-cross-bin distance, in contrast with previous bin-to-bin distances and cross-bin distances. The BRD is robust to partial matching and histogram normalization, and captures correlations between bins with only a linear computational complexity. We combine the BRD with the ℓ1 histogram distance and the χ2 histogram distance to generate the ℓ1 BRD and the χ2 BRD, respectively. These combinations exploit and benefit from the robustness of the BRD under partial matching and the robustness of the ℓ1 and χ2 distances to small noise. We propose a method for assessing the robustness of histogram distances to partial matching. The BRDs and logistic regression-based histogram fusion are applied to image classification. The experimental results on synthetic data sets show the robustness of the BRDs to partial matching, and the experiments on seven benchmark data sets demonstrate promising results of the BRDs for image classification.