@inproceedings{c249e9a941bf42c7939670ff2087ee37,
title = "Robust anisotropic diffusion: Connections between robust statistics, line processing, and anisotropic diffusion",
abstract = "Relations between anisotropic diffusion and robust statistics are described in this paper. We show that anisotropic diffusion can be seen as a robust estimation procedure that estimates a piecewise smooth image from a noisy input image. The {"}edge-stopping{"} function in the anisotropic diffusion equation is closely related to the error norm and influence function in the robust estimation framework. This connection leads to a new {"}edge-stopping{"} function based on Tukey's biweightrobust estimator, that preserves sharper boundaries than previous formulations and improves the automatic stopping of the diffusion. The robust statistical interpretation also provides a means for detecting the boundaries (edges) between the piecewise smooth regions in the image. Finally, connections between robust estimation and line processing provide a framework to introduce spatial coherence in anisotropic diffusion flows.",
author = "Black, {M. J.} and G. Sapiro and D. Marimont and D. Heeger",
year = "1997",
doi = "10.1007/3-540-63167-4_27",
language = "English (US)",
isbn = "3540631674",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "323--326",
editor = "{ter Haar Romeny}, Bart and Max Viergever and Luc Florack and Jan Koenderink",
booktitle = "Scale-Space Theory in Computer Vision - 1st International Conference, Scale-Space 1997, Proceedings",
note = "1st International Conference on Scale-Space Theory in Computer Vision, Scale-Space 1997 ; Conference date: 02-07-1997 Through 04-07-1997",
}