Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
Solution of nonlinear diffusion appearing in image smoothing and edge detection
Applied Numerical Mathematics
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Images as Embedded Maps and Minimal Surfaces: Movies, Color, Texture, and Volumetric Medical Images
International Journal of Computer Vision - Special issue on computer vision research at the Technion
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
Gabor Feature Space Diffusion via the Minimal Weighted Area Method
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
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
SIAM Journal on Numerical Analysis
Towards a theoretical foundation for Laplacian-based manifold methods
Journal of Computer and System Sciences
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
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
Anisotropic α-kernels and associated flows
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Regularity and scale-space properties of fractional high order linear filtering
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Stochastic differential equations and geometric flows
IEEE Transactions on Image Processing
Estimation of optimal PDE-based denoising in the SNR sense
IEEE Transactions on Image Processing
A Short- Time Beltrami Kernel for Smoothing Images and Manifolds
IEEE Transactions on Image Processing
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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, Felsberg, Florack, and Platel [$\alpha$ scale spaces on a bounded domain, in Scale Space Methods in Computer Vision, L. D. Griffin and M. Lillholm, eds., Lecture Notes in Comput. Sci. 2695, Springer, Berlin, Heidelberg, 2003, pp. 494-510] and Duits, Florack, de Graaf, and ter Haar Romeny [J. Math. Imaging Vision, 20 (2004), pp. 267-298]. 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 and Beltrami flows along with their properties.