Numerical Schemes of Shock Filter Models for Image Enhancement and Restoration
Journal of Mathematical Imaging and Vision
A Note on Two Classical Enhancement Filters and Their Associated PDE's
International Journal of Computer Vision
Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Regularized Shock Filters and Complex Diffusion
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Numerical Solution Schemes for Continuous-Scale Morphology
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Curvature-Driven PDE Methods for Matrix-Valued Images
International Journal of Computer Vision
A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion
Journal of Mathematical Imaging and Vision
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Morphology for matrix data: Ordering versus PDE-based approach
Image and Vision Computing
A generic approach to diffusion filtering of matrix-fields
Computing - Special Issue on Industrial Geometry
Anisotropic Continuous-Scale Morphology
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
PDE-Driven Adaptive Morphology for Matrix Fields
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Visualization and Processing of Tensor Fields: Advances and Perspectives
Visualization and Processing of Tensor Fields: Advances and Perspectives
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
Image and Vision Computing
Novel schemes for hyperbolic PDEs using osmosis filters from visual computing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
| Hi-index | 0.00 |
In this article we consider adaptive, PDE-driven morphological operations for 3D matrix fields arising e.g. in diffusion tensor magnetic resonance imaging (DT-MRI). The anisotropic evolution is steered by a matrix constructed from a structure tensor for matrix valued data. An important novelty is an intrinsically one-dimensional directional variant of the matrix-valued upwind schemes such as the Rouy-Tourin scheme. It enables our method to complete or enhance anisotropic structures effectively. A special advantage of our approach is that upwind schemes are utilised only in their basic one-dimensional version, hence avoiding grid effects and leading to an accurate algorithm. No higher dimensional variants of the schemes themselves are required. Experiments with synthetic and real-world data substantiate the gap-closing and line-completing properties of the proposed method.