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.

翻译：金字塔变换是一种以多尺度方式分析序列的构造性方法。传统上，这些变换依赖于平稳的上采样和下采样操作。本文提出采用非平稳细分格式作为随细化层级变化的上采样算子。这些格式提供了更大的灵活性，使得开发先进的多尺度变换（包括几何多尺度分析）成为可能。我们建立了这些非平稳算子的基本性质，并证明了它们在捕捉和分析几何特征方面的有效性。特别地，我们展示了其在检测平面物体几何结构中的应用，以突显其实用性。