Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
Pseudo-Linear Scale-Space Theory
International Journal of Computer Vision
Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
The curve indicator random field
The curve indicator random field
On the Axioms of Scale Space Theory
Journal of Mathematical Imaging and Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space
Journal of Mathematical Imaging and Vision
Maxwell strata in the Euler elastic problem
Journal of Dynamical and Control Systems
Regularizing Flows over Lie Groups
Journal of Mathematical Imaging and Vision
PDE-Driven Adaptive Morphology for Matrix Fields
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
A Directional Rouy-Tourin Scheme for Adaptive Matrix-Valued Morphology
ISMM '09 Proceedings of the 9th International Symposium on Mathematical Morphology and Its Application to Signal and Image Processing
Crossing-Preserving Coherence-Enhancing Diffusion on Invertible Orientation Scores
International Journal of Computer Vision
Brain Connectivity Mapping Using Riemannian Geometry, Control Theory, and PDEs
SIAM Journal on Imaging Sciences
An explanation for the logarithmic connection between linear and morphological systems
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Families of generalised morphological scale spaces
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
International Journal of Computer Vision
International Journal of Computer Vision
From stochastic completion fields to tensor voting
DSSCV'05 Proceedings of the First international conference on Deep Structure, Singularities, and Computer Vision
Denoising tensors via lie group flows
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
Numerical schemes for linear and non-linear enhancement of DW-MRI
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Mathematical Methods for Signal and Image Analysis and Representation
Mathematical Methods for Signal and Image Analysis and Representation
Accelerated diffusion operators for enhancing DW-MRI
EG VCBM'10 Proceedings of the 2nd Eurographics conference on Visual Computing for Biology and Medicine
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We consider morphological and linear scale spaces on the space 驴3驴S 2 of 3D positions and orientations naturally embedded in the group SE(3) of 3D rigid body movements. The general motivation for these (convection-)diffusions and erosions is to obtain crossing-preserving fiber enhancement on probability densities defined on the space of positions and orientations. The strength of these enhancements is that they are expressed in a moving frame of reference attached to fiber fragments, allowing us to diffuse along the fibers and to erode orthogonal to them.The linear scale spaces are described by forward Kolmogorov equations of Brownian motions on 驴3驴S 2 and can be solved by convolution with the corresponding Green's functions. The morphological scale spaces are Bellman equations of cost processes on 驴3驴S 2 and we show that their viscosity solutions are given by a morphological convolution with the corresponding morphological Green's function.For theoretical underpinning of our scale spaces on 驴3驴S 2 we introduce Lagrangians and Hamiltonians on 驴3驴S 2 indexed by a parameter 驴驴[1,驴). The Hamiltonian induces a Hamilton-Jacobi-Bellman system that coincides with our morphological scale spaces on 驴3驴S 2.By means of the logarithm on SE(3) we provide tangible estimates for both the linear- and the morphological Green's functions. We also discuss numerical finite difference upwind schemes for morphological scale spaces (erosions) of Diffusion-Weighted Magnetic Resonance Imaging (DW-MRI), which allow extensions to data-adaptive erosions of DW-MRI.We apply our theory to the enhancement of (crossing) fibres in DW-MRI for imaging water diffusion processes in brain white matter.