Nonlinear Approximation of Spatiotemporal Data Using Diffusion Wavelets

摘要

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 L~2 functions on graphs. This permits the study of classical wavelet algorithms (such as compression and denoising of functions in L~2(R~n), 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 as 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.