Trilateral filter on graph spectral domain

This paper presents the trilateral filter (TF) in the perspective of graph signal processing. The TF is a single-pass nonlocal filter for edge-preserving smoothing. To smooth an image, it does not require many iterations compared to conventional smoothing methods, e.g., the bilateral filter. Additionally, one parameter is only required for filtering. Since the TF coefficients depend on original image data, it is not possible to provide a frequency domain representation using regular signal processing. To overcome this problem, we firstly show the TF as a vertex domain transform on a graph and then define it on graph spectral domain. In the experimental results, the proposed method presents better denoising performances than conventional methods.