An Efficient Coding of Three Dimensional Colour Distributions for Image Retrieval

The distribution of colours in an image provides a useful cue for image indexing and object recognition [1,3,2,4]. Previously, we have shown how chromaticity distributions can be coded using a hybrid compression technique: histograms are coded with a Discrete Cosine Transform and then Principal Component Analysis is applied to a reduced set of the DCT coefficients, resulting in excellent indexing results, using just the first eight Principal Components [5,6]. We have investigated compression on colour distributions independent of colour intensity, however, colour is generally represented by a 3-D model, (two chromaticity channels and one intensity channel). One difficulty with 3-D chromaticity distribution histograms is their sparseness - many bins contain no or few image pixels. This becomes a problem when attempting to derive PCA statistics: it becomes necessary to analyse an unrealistically large number of histograms. We show that applying the Discrete Fourier Transform to colour distribution histograms leads to a dimensionality reduction that makes PCA possible. We also demonstrate the general case that 3-D and n-D distributions, particularly sparse ones, can be significantly reduced in dimension.