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Proceedings Paper

Invariance of edges and corners under mean-curvature diffusions of images
Author(s): Adel I. El-Fallah; Gary E. Ford; V. Ralph Algazi; Robert R. Estes Jr.
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Paper Abstract

We have recently proposed the use of geometry in image processing by representing an image as a surface in 3-space. The linear variations in intensity (edges) were shown to have a nondivergent surface normal. Exploiting this feature we introduced a nonlinear adaptive filter that only averages the divergence in the direction of the surface normal. This led to an inhomogeneous diffusion (ID) that averages the mean curvature of the surface, rendering edges invariant while removing noise. This mean curvature diffusion (MCD) when applied to an isolated edge imbedded in additive Gaussian noise results in complete noise removal and edge enhancement with the edge location left intact. In this paper we introduce a new filter that will render corners (two intersecting edges), as well as edges, invariant to the diffusion process. Because many edges in images are not isolated the corner model better represents the image than the edge model. For this reason, this new filtering technique, while encompassing MCD, also outperforms it when applied to images. Many applications will benefit from this geometrical interpretation of image processing, and those discussed in this paper include image noise removal, edge and/or corner detection and enhancement, and perceptually transparent coding.

Paper Details

Date Published: 23 March 1995
PDF: 13 pages
Proc. SPIE 2421, Image and Video Processing III, (23 March 1995); doi: 10.1117/12.205467
Show Author Affiliations
Adel I. El-Fallah, Univ. of California/Davis (United States)
Gary E. Ford, Univ. of California/Davis (United States)
V. Ralph Algazi, Univ. of California/Davis (United States)
Robert R. Estes Jr., Univ. of California/Davis (United States)

Published in SPIE Proceedings Vol. 2421:
Image and Video Processing III
Robert L. Stevenson; Sarah A. Rajala, Editor(s)

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