Efficient Descriptors of Hue Distributions from Kernel Density Estimators and Fourier Transforms

Many color-based image retrieval systems define the similarity (with regard to color) between two images as the similarity between the probability distributions of the color vectors in the images. These probability distributions are almost always estimated by histograms. Histograms have however the disadvantage that they are discontinuous and their form depends on the selection of the histogram bins. Results from probability theory and statistics show that kernel-based estimators are superior to the histogram in many respects. Previous studies in image retrieval have however shown that a naive application of kernel-based estimators provide no improvement in retrieval performance. In this paper we first motivate why a combination of kernel-based estimators and Fourier transform theory provides good estimators of the similarity of hue-distributions. We then show that Fourier coefficients provide efficient descriptors of the probability distributions and that these Fourier coefficients can be directly used to compute the similarity between the hue distributions of images. Next we describe two methods to select the most relevant Fourier coefficients for image retrieval. We will argue that in image retrieval we should not select those Fourier coefficients that are most important for the description of the probability distributions themselves but that we should select those coefficients that are most important in the estimation of the difference between similar distributions. In the experimental part of the paper we describe the performance of these kernel-based methods when they are applied to image retrieval tasks involving the MPEG7 image database. We will show that the retrieval performance of the kernel based method is better than the performance of histogram methods and we will show that the retrieval performance is also relatively insensitive to the choice of the Kernel and the width of the Kernel.