Analysis of Multiresolution Representations for Compression and Local Description of Images

Abstract

Low level features of images are often extracted from their representations in a Gaussian scale space. These representations satisfy the desired properties of covariance under a set of transformations (translations, rotations, scale changes) as well as of causality. However, the corresponding image representations, due to their redundant and non sparse nature, are not well suited for compression purposes. This paper aims at characterizing a set of multiresolution representations from the joint perspective of feature point and descriptor extraction and of compression. This analysis leads to the design of a feature point detector and of a local descriptor in signal representations given by oversampled steerable transforms. It is shown that the steerable transforms due to their properties of covariance under translations, and rotations as well as of angular selectivity provide signal representations well suited to address the signal description problem. At the same time, techniques such as iterative projection algorithms (POCS – projection on convex sets) are used to reduce the coding cost induced by the corresponding oversampled signal representation. The robustness and the discriminative power of extracted features are rated in terms of the entropy of the quantized representation. These results show the tradeoff that can be found between compression and description.