Nonlinear approximation of spatiotemporal data using diffusion wavelets

Abstract

We present a multiscale, graph-based approach to 3D image analysis using diffusion wavelet bases, which were presented in [1]. Diffusion wavelets allow to obtain orthonormal bases of L2 functions on graphs. This permits the study of classical wavelet algorithms (such as compression and denoising of functions in L2(ℝn), n ∈ ℕ, via nonlinear approximation) in this setting. In this paper, we describe how this could be used in structure-preserving compression of image sequences, modelled as a whole EIS a weighted graph, as a first step towards structural spatiotemporal wavelet segmentation. We further discuss the possibilities for using this abstract approach in computer vision tasks. © Springer-Verlag Berlin Heidelberg 2007.