Efficient Color Histogram Indexing for Quadratic Form Distance Functions

In image retrieval based on color, the weighted distance between color histograms of two images, represented as a quadratic form, may be defined as a match measure. However, this distance measure is computationally expensive (naively O(N2) and at best O(N) in the number N of histogram bins) and it operates on high dimensional features (O(N)). We propose the use of low-dimensional, simple to compute distance measures between the color distributions, and show that these are lower bounds on the histogram distance measure. Results on color histogram matching in large image databases show that prefiltering with the simpler distance measures leads to significantly less time complexity because the quadratic histogram distance is now computed on a smaller set of images. The low-dimensional distance measure can also be used for indexing into the database.