Orientation Diffusion or How to Comb a Porcupine

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 S1. Applications to color analysis are discussed and numerical experiments demonstrate again the power of the Beltrami framework for nontrivial geometries in image processing.

[1]  Yehoshua Y. Zeevi,et al.  Representation of colored images by manifolds embedded in higher dimensional non-Euclidean space , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[2]  Yehoshua Y. Zeevi,et al.  A Geometric Functional for Derivatives Approximation , 1999, Scale-Space.

[3]  Joachim Weickert,et al.  Coherence-enhancing diffusion of colour images , 1999, Image Vis. Comput..

[4]  A. Polyakov Quantum Geometry of Bosonic Strings , 1981 .

[5]  Guillermo Sapiro,et al.  Direction diffusion , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[6]  Bart M. ter Haar Romeny,et al.  Geometry-Driven Diffusion in Computer Vision , 1994, Computational Imaging and Vision.

[7]  Alvy Ray Smith,et al.  Color gamut transform pairs , 1978, SIGGRAPH.

[8]  Pietro Perona Orientation diffusions , 1998, IEEE Trans. Image Process..

[9]  Ron Kimmel,et al.  A general framework for low level vision , 1998, IEEE Trans. Image Process..

[10]  Guillermo Sapiro,et al.  Color image enhancement via chromaticity diffusion , 2001, IEEE Trans. Image Process..

[11]  Ron Kimmel,et al.  From High Energy Physics to Low Level Vision , 1997, Scale-Space.

[12]  Ron Kimmel,et al.  Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images , 2000, International Journal of Computer Vision.

[13]  Tony F. Chan,et al.  Variational Restoration of Nonflat Image Features: Models and Algorithms , 2001, SIAM J. Appl. Math..

[14]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .