Pyramid transforms via nonstationary subdivision schemes

TL;DR

This paper introduces nonstationary subdivision schemes for pyramid transforms, enhancing multiscale analysis by capturing geometric features more effectively than traditional stationary methods.

Contribution

It proposes a novel use of nonstationary subdivision schemes as upsampling operators in pyramid transforms, enabling advanced geometric multiscale analysis.

Findings

Effective in capturing geometric features

Applicable to detecting structures in planar objects

Demonstrates flexibility over stationary 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.