Mapping images to a high-dimensional feature space, either by considering patches of images or other features, has lead to state-of-art results in signal processing tasks such as image denoising and imprinting, and in various machine learning and computer vision tasks on images. Understanding the geometry of the embedding of images into high-dimensional feature space is a challenging problem. Finding efficient representations and learning dictionaries for such embeddings is also problematic, often leading to expensive optimization algorithms. Many such algorithms scale poorly with the dimension of the feature space, for example with the size of patches of images if these are chosen as features. This is in contrast with the crucial needs of using a multi-scale approach in the analysis of images, as details at multiple scales are crucial in image understanding, as well as in many signal processing tasks. Here we exploit a recent dictionary learning algorithm based on Geometric Wavelets, and we extend it to perform multi-scale dictionary learning on image patches, with efficient algorithms for both the learning of the dictionary, and the computation of coefficients onto that dictionary. We also discuss how invariances in images may be introduced in the dictionary learning phase, by generalizing the construction of such dictionaries to non-Euclidean spaces.

Date Published: 5 October 2013
PDF: 23 pages
Proc. SPIE 8858, Wavelets and Sparsity XV, 88581T (5 October 2013); doi: 10.1117/12.2021984

Published in SPIE Proceedings Vol. 8858:
Wavelets and Sparsity XV
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)