Pyramid transforms via nonstationary subdivision schemes

Abstract: Pyramid transforms are constructive methods for analyzing sequences in a multiscale fashion. Traditionally, these transforms rely on stationary upsampling and downsampling operations. In this paper, we propose employing nonstationary subdivision schemes as upsampling operators that vary according to the refinement level. These schemes offer greater flexibility, enabling the development of advanced multiscale transforms, including geometric multiscale analysis. We establish the fundamental properties of these nonstationary operators and demonstrate their effectiveness in capturing and analyzing geometric features. In particular, we present applications to highlight their utility in detecting geometric structures in planar objects.