Читать книгу Graph Spectral Image Processing - Gene Cheung - Страница 26

This book (especially this chapter) focuses on graph spectral domain operations for image processing. Here, we describe interconnections between well-studied edge preserving filters and their GSP-based representations. As previously mentioned in this section, pixel-dependent filters do not have frequency domain expressions in a classical sense. This is because the impulse responses vary for different pixel index values n. In the following, we show that such a pixel-dependent filter can be viewed as a graph spectral filter, i.e. it presents a diagonal graph frequency response. Roughly speaking, GSP-based image processing considers the pixel structure and the filter kernel independently. Therefore, the pixel-dependent processing can be performed with a fixed filter kernel, owing to the underlying graph.