Sparse Multiscale Patches for Image Processing

This paper presents a framework to define an objective measure of the similarity (or dissimilarity) between two images for image processing. The problem is twofold: 1) define a set of features that capture the information contained in the image relevant for the given task and 2) define a similarity measure in this feature space. In this paper, we propose a feature space as well as a statistical measure on this space. Our feature space is based on a global descriptor of the image in a multiscale transformed domain. After decomposition into a Laplacian pyramid, the coefficients are arranged in intrascale/interscale/interchannel patches which reflect the dependencies of neighboring coefficients in presence of specific structures or textures. At each scale, the probability density function (pdf) of these patches is used as a descriptor of the relevant information. Because of the sparsity of the multiscale transform, the most significant patches, called Sparse Multiscale Patches (SMP), describe efficiently these pdfs. We propose a statistical measure (the Kullback-Leibler divergence) based on the comparison of these probability density functions. Interestingly, this measure is estimated via the nonparametric, k-th nearest neighbor framework without explicitly building the pdfs. This framework is applied to a query-by-example image retrieval method. Experiments on two publicly available databases showed the potential of our SMP approach for this task. In particular, it performed comparably to a SIFT -based retrieval method and two versions of a fuzzy segmentation-based method (the UFM and CLUE methods), and it exhibited some robustness to different geometric and radiometric deformations of the images.