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 biweight robust 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. We extend the framework to vector-valued images and show applications to robust image sharpening.
| Original language | English (US) |
|---|---|
| Title of host publication | IEEE International Conference on Image Processing |
| Publisher | IEEE Comp Soc |
| Pages | 263-266 |
| Number of pages | 4 |
| Volume | 1 |
| State | Published - 1997 |
| Event | Proceedings of the 1997 International Conference on Image Processing. Part 2 (of 3) - Santa Barbara, CA, USA Duration: Oct 26 1997 → Oct 29 1997 |
Other
| Other | Proceedings of the 1997 International Conference on Image Processing. Part 2 (of 3) |
|---|---|
| City | Santa Barbara, CA, USA |
| Period | 10/26/97 → 10/29/97 |
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ASJC Scopus subject areas
- Computer Vision and Pattern Recognition
- Hardware and Architecture
- Electrical and Electronic Engineering
Cite this
Robust anisotropic diffusion and sharpening of scalar and vector images. / Black, Michael; Sapiro, Guillermo; Marimont, David; Heeger, David.
IEEE International Conference on Image Processing. Vol. 1 IEEE Comp Soc, 1997. p. 263-266.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Robust anisotropic diffusion and sharpening of scalar and vector images
AU - Black, Michael
AU - Sapiro, Guillermo
AU - Marimont, David
AU - Heeger, David
PY - 1997
Y1 - 1997
N2 - 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 biweight robust 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. We extend the framework to vector-valued images and show applications to robust image sharpening.
AB - 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 biweight robust 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. We extend the framework to vector-valued images and show applications to robust image sharpening.
UR - http://www.scopus.com/inward/record.url?scp=0031335083&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0031335083&partnerID=8YFLogxK
M3 - Conference contribution
AN - SCOPUS:0031335083
VL - 1
SP - 263
EP - 266
BT - IEEE International Conference on Image Processing
PB - IEEE Comp Soc
ER -