Computer Vision, Graphics, and Image Processing
Topics in matrix analysis
Image Analysis Using Mathematical Morphology
IEEE Transactions on Pattern Analysis and Machine Intelligence
A nonlinear laplace operator as edge detector in noisy images
Computer Vision, Graphics, and Image Processing
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Computing oriented texture fields
CVGIP: Graphical Models and Image Processing
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
Morphological operators for image sequences
Computer Vision and Image Understanding
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Complete ordering and multivariate mathematical morphology
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Vector Median Filters, Inf-Sup Operations, and Coupled PDE's: Theoretical Connections
Journal of Mathematical Imaging and Vision
Signal Processing for Computer Vision
Signal Processing for Computer Vision
Computational Framework for Segmentation and Grouping
Computational Framework for Segmentation and Grouping
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
Regularized Laplacian Zero Crossings as Optimal Edge Integrators
International Journal of Computer Vision
Regularized Shock Filters and Complex Diffusion
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
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
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Digital Step Edges from Zero Crossing of Second Directional Derivatives
IEEE Transactions on Pattern Analysis and Machine Intelligence
A comparative study on multivariate mathematical morphology
Pattern Recognition
Graph-based morphological processing of multivariate microscopy images and data bases
ISBI'10 Proceedings of the 2010 IEEE international conference on Biomedical imaging: from nano to Macro
Barankin-type lower bound on multiple change-point estimation
IEEE Transactions on Signal Processing
Adaptive Continuous-Scale Morphology for Matrix Fields
International Journal of Computer Vision
Recursive structure element decomposition using migration fitness scaling genetic algorithm
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part I
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Positive semidefinite matrix fields are becoming increasingly important in digital imaging. One reason for this tendency is the introduction of diffusion tensor magnetic resonance imaging (DT-MRI). In order to perform shape analysis, enhancement or segmentation of such tensor/matrix fields, appropriate image processing tools must be developed. This paper extends fundamental morphological operations to the matrix-valued setting. We start by presenting novel definitions for the supremum and infimum of a set of matrices since these notions lie at the heart of the morphological operations. In contrast to naive approaches like the component-wise maximum or minimum of the matrix channels, our approach is based on the Loewner ordering for symmetric matrices. The notions of supremum and infimum deduced from this partial ordering satisfy desirable properties such as rotation invariance, preservation of positive semidefiniteness, and continuous dependence on the input data. We introduce erosion, dilation, opening, closing, top hats, morphological derivatives, shock filters, and mid-range filters for positive semidefinite matrix-valued images. These morphological operations incorporate information simultaneously from all matrix channels rather than treating them independently. Experiments on DT-MRI images with ball- and rod-shaped structuring elements illustrate the properties and performance of our morphological operators for matrix-valued data.