Matrix analysis
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
Constrained Flows of Matrix-Valued Functions: Application to Diffusion Tensor Regularization
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Total Variation Minimization by the Fast Level Sets Transform
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Curvature-Driven PDE Methods for Matrix-Valued Images
International Journal of Computer 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
Image and Vision Computing
Fast and simple calculus on tensors in the log-euclidean framework
MICCAI'05 Proceedings of the 8th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Flexible segmentation and smoothing of DT-MRI fields through a customizable structure tensor
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
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There is an increasing demand to develop image processing tools for the filtering and analysis of matrix-valued data, so-called matrix fields. In the case of scalar-valued images parabolic partial differential equations (PDEs) are widely used to perform filtering and denoising processes. Especially interesting from a theoretical as well as from a practical point of view are PDEs with singular diffusivities describing processes like total variation (TV-)diffusion, mean curvature motion and its generalisation, the so-called self-snakes. In this contribution we propose a generic framework that allows us to find the matrix-valued counterparts of the equations mentioned above. In order to solve these novel matrix-valued PDEs successfully we develop truly matrix-valued analogs to numerical solution schemes of the scalar setting. Numerical experiments performed on both synthetic and real world data substantiate the effectiveness of our matrix-valued, singular diffusion filters.