Unconditionally Stable Shock Filters for Image and Geometry Processing

• Published in: Computer graphics forum Vol. 34; no. 5; pp. 201 - 210
• Main Authors: Prada, F., Kazhdan, M.
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.08.2015
• Subjects: Advection; Analysis; Categories and Subject Descriptors (according to ACM CCS); Computer graphics; Filtering; Filtration; Geometry; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Hierarchy and geometric transformations; I.4.3 [Image Processing and Computer Vision]: Enhancement-Sharpening and deblurring; Image processing systems; Robustness; Signal processing; Studies; Three dimensional
• ISSN: 0167-7055; 1467-8659
• DOI: 10.1111/cgf.12708

This work revisits the Shock Filters of Osher and Rudin [OR90] and shows how the proposed filtering process can be interpreted as the advection of image values along flow‐lines. Using this interpretation, we obtain an efficient implementation that only requires tracing flow‐lines and re‐sampling the image. We show that the approach is stable, allowing the use of arbitrarily large time steps without requiring a linear solve. Furthermore, we demonstrate the robustness of the approach by extending it to the processing of signals on meshes in 3D.