Orientation Diffusion or How to Comb a Porcupine

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 approach the orientation denoising problem via the geometric Beltrami framework for image processing. The feature (orientation) 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) space is the unit circle S 1 . Applications to color analysis are discussed and numerical experiments demonstrate again the power of the Beltrami framework for nontrivial geometries in image processing. C 2002 Elsevier Science (USA)

Anisotropic Smoothing Using Double Orientations

“…Note that as in [16] the curvature-based method can include multiple directions. Various papers deal with the smoothing of normal vectors by minimizing certain energy functionals [17,18,19,20,21,22] and use this information for subsequent denoising. In general these minimization procedures are much more expensive then our double direction approach.…”

Gabor Feature Space Diffusion via the Minimal Weighted Area Method

“…We explore the behavior of each parameter when considered separately, and also the coupling between these parameters. Another natural continuation of this work is to apply the results of Kimmel and Sochen [14] in order to obtain a more robust orientation diffusion where the orientations manifold is embedded in R 2 ⊗ S 1 . By properly choosing the local coordinate systems for both manifolds the problem arising from the cyclic nature of angles is addressed.…”

Equalized Net Diffusion (END) for the Preservation of Fine Structures in PDE-based Image Restoration

“…It is clear to see that the net diffusion of the above model is in the form of (17). The suggested ND function (17) is our choice of function which satisfies all the desirable properties (P1)~(P4); it will be interesting to find more effective ND function.…”

“…There have been various partial differential equation (PDE)-based restoration models such as the Perona-Malik model [25] , the total variation (TV) model [18,26] , and color restoration models [3,10,15,17,28] . These PDE-based models have been extensively studied to answer fundamental questions in image restoration and have allowed researchers and practitioners not only to introduce new mathematical models but also to improve traditional algorithms [1,4,9,22,30] .…”