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 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.>

The successive refinement of information consists of first approximating data using a few bits of information, then iteratively improving the approximation as more and more information is supplied. The goal is to achieve an optimal description at each stage. In general, an ongoing description which is rate-distortion optimal whenever it is interrupted is sought. It is shown that in order to achieve optimal successive refinement the necessary and sufficient conditions are that the solutions of the rate distortion problem can be written as a Markov chain. In particular, all finite alphabet signals with Hamming distortion satisfy these requirements. It is also shown that the same is true for Gaussian signals with squared error distortion and for Laplacian signals with absolute error distortion. A simple counterexample with absolute error distortion and a symmetric source distribution which shows that successive refinement is not always achievable is presented.>

Two methods for reducing the computation involved in vector quantization picture coding are presented. First, a data structure (k-d trees, developed by Bentley) is demonstrated to be appropriate for implementing exact nearest neighbor searching in time logarithmic in codebook size. Second, the Pairwise Nearest Neighbor (PNN) algorithm is presented as an alternative to the generalized Lloyd (Linde-Buzo-Gray) algorithm. The PNN algorithm derives a vector quantization codebook in a diminishingly small fraction of the time previously required, without sacrificing performance. Simulations on a variety of images coded at 1/2 bit per pixel indicate that PNN codebooks can be developed in roughly 5% of the time required by the LBG algorithm. The PNN algorithm can be used with squared error and weighted squared error distortion measures. These results are generalizable to any vector quantization application with the appropriate distortion measure.