Invariance of edges and corners under mean-curvature diffusions of images

Adel I. El-Fallah; Gary E. Ford; V. Ralph Algazi; Robert R. Estes Jr.

doi:10.1117/12.205467

23 March 1995 Invariance of edges and corners under mean-curvature diffusions of images

Adel I. El-Fallah, Gary E. Ford, V. Ralph Algazi, Robert R. Estes Jr.

Proceedings Volume 2421, Image and Video Processing III; (1995) https://doi.org/10.1117/12.205467
Event: IS&T/SPIE's Symposium on Electronic Imaging: Science and Technology, 1995, San Jose, CA, United States

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.

Citation Download Citation

Adel I. El-Fallah, Gary E. Ford, V. Ralph Algazi, and Robert R. Estes Jr. "Invariance of edges and corners under mean-curvature diffusions of images", Proc. SPIE 2421, Image and Video Processing III, (23 March 1995); https://doi.org/10.1117/12.205467

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