Handbook of image processing operators
Handbook of image processing operators
Vector Median Filters, Inf-Sup Operations, and Coupled PDE's: Theoretical Connections
Journal of Mathematical Imaging and Vision
Nonlinear Filters for Image Processing
Nonlinear Filters for Image Processing
Regularization of MR Diffusion Tensor Maps for Tracking Brain White Matter Bundles
MICCAI '98 Proceedings of the First International Conference on Medical Image Computing and Computer-Assisted Intervention
Image Processing for Diffusion Tensor Magnetic Resonance Imaging
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Edge Preserving Regularization and Tracking for Diffusion Tensor Imaging
MICCAI '01 Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention
Nonlinear Matrix Diffusion for Optic Flow Estimation
Proceedings of the 24th DAGM Symposium on Pattern Recognition
Binary Partitioning, Perceptual Grouping, and Restoration with Semidefinite Programming
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
On the Continuous Fermat-Weber Problem
Operations Research
Least squares and robust estimation of local image structure
Scale Space'03 Proceedings of the 4th international conference on Scale space methods in computer vision
Matrix-valued filters as convex programs
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
A quasi-Euclidean norm to speed up vector median filtering
IEEE Transactions on Image Processing
One-iteration dejittering of digital video images
Journal of Visual Communication and Image Representation
Fast Dejittering for Digital Video Frames
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
New Riemannian techniques for directional and tensorial image data
Pattern Recognition
A Study of Parts-Based Object Class Detection Using Complete Graphs
International Journal of Computer Vision
On vector and matrix median computation
Journal of Computational and Applied Mathematics
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We develop a concept for the median filtering of tensor data. The main part of this concept is the definition of median for symmetric matrices. This definition is based on the minimisation of a geometrically motivated objective function which measures the sum of distances of a variable matrix to the given data matrices. This theoretically well-founded concept fits into a context of similarly defined median filters for other multivariate data. Unlike some other approaches, we do not require by definition that the median has to be one of the given data values. Nevertheless, it happens so in many cases, equipping the matrix-valued median even with root signals similar to the scalar-valued situation. Like their scalar-valued counterparts, matrix-valued median filters show excellent capabilities for structure-preserving denoising. Experiments on diffusion tensor imaging, fluid dynamics and orientation estimation data are shown to demonstrate this. The orientation estimation examples give rise to a new variant of a robust adaptive structure tensor which can be compared to existing concepts. For the efficient computation of matrix medians, we present a convex programming framework. By generalising the idea of the matrix median filters, we design a variety of other local matrix filters. These include matrix-valued mid-range filters and, more generally, M-smoothers but also weighted medians and @a-quantiles. Mid-range filters and quantiles allow also interesting cross-links to fundamental concepts of matrix morphology.