Technical Report CIS-2000-02

Title: Orientation Diffusion or How to Comb a Porcupine?
Authors: Ron Kimmel & Nir Sochen
Abstract: This paper addresses the problem of feature enhancement in noisy images, when the feature is known to be constrained to a manifold. As an example, we present the orientation diffusion as a derivation of the geometric Beltrami framework for image processing. The feature field is represented accordingly as the embedding of a two dimensional surface in the spatial-feature manifold. The resulted Beltrami flow is a selective smoothing process that respects the feature constraint. Orientation diffusion is treated as a canonical example where the feature (orientation in this case) spaces are the unit circle $S^1$, the unit sphere $S^2$, and the unit hyper-sphere $S^n$. Applications to color analysis are discussed and numerical experiments demonstrate again the power of the Beltrami framework for non-trivial geometries in image processing.
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