Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Applied numerical linear algebra
Applied numerical linear algebra
Linear Scale-Space has First been Proposed in Japan
Journal of Mathematical Imaging and Vision
An Extended Class of Scale-Invariant and Recursive Scale Space Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
IMPLICITLY RESTARTED ARNOLDI/LANCZOS METHODS FOR LARGE SCALE EIGENVALUE CALCULATIONS
IMPLICITLY RESTARTED ARNOLDI/LANCZOS METHODS FOR LARGE SCALE EIGENVALUE CALCULATIONS
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
The Monogenic Scale-Space: A Unifying Approach to Phase-Based Image Processing in Scale-Space
Journal of Mathematical Imaging and Vision
The monogenic scale space on a bounded domain and its applications
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
α scale spaces on a bounded domain
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Stochastic differential equations and geometric flows
IEEE Transactions on Image Processing
Anisotropic $\alpha$-Kernels and Associated Flows
SIAM Journal on Imaging Sciences
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The Laplacian raised to fractional powers can be used to generate scale spaces as was shown in recent literature by Duits et al. In this paper, we study the anisotropic diffusion processes by defining new generators that are fractional powers of an anisotropic scale space generator. This is done in a general framework that allows us to explain the relation between a differential operator that generates the flow and the generators that are constructed from its fractional powers. We then generalize this to any other function of the operator. We discuss important issues involved in the numerical implementation of this framework and present several examples of fractional versions of the Perona-Malik flow along with their properties.