ISSN:
1573-1405
Keywords:
directions
;
isotropic and anisotropic diffusion
;
multiscale representations
;
harmonic maps
;
general non-flat manifolds
;
liquid crystals
;
gradients
;
optical flow
;
color images
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract In a number of disciplines, directional data provides a fundamental source of information. A novel framework for isotropic and anisotropic diffusion of directions is presented in this paper. The framework can be applied both to denoise directional data and to obtain multiscale representations of it. The basic idea is to apply and extend results from the theory of harmonic maps, and in particular, harmonic maps in liquid crystals. This theory deals with the regularization of vectorial data, while satisfying the intrinsic unit norm constraint of directional data. We show the corresponding variational and partial differential equations formulations for isotropic diffusion, obtained from an L2 norm, and edge preserving diffusion, obtained from an L norm in general and an L1 norm in particular. In contrast with previous approaches, the framework is valid for directions in any dimensions, supports non-smooth data, and gives both isotropic and anisotropic formulations. In addition, the framework of harmonic maps here described can be used to diffuse and analyze general image data defined on general non-flat manifolds, that is, functions between two general manifolds. We present a number of theoretical results, open questions, and examples for gradient vectors, optical flow, and color images.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008152115986
