Matrix analysis
A note on the gradient of a multi-image
Computer Vision, Graphics, and Image Processing - Lectures notes in computer science, Vol. 201 (G. Goos and J. Hartmanis, Eds.)
Multidimensional Orientation Estimation with Applications to Texture Analysis and Optical Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
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
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
ACIVS '08 Proceedings of the 10th International Conference on Advanced Concepts for Intelligent Vision Systems
PDE-Driven Adaptive Morphology for Matrix Fields
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Image and Vision Computing
Highly Accurate Schemes for PDE-Based Morphology with General Convex Structuring Elements
International Journal of Computer Vision
Adaptive Continuous-Scale Morphology for Matrix Fields
International Journal of Computer Vision
Morphological and Linear Scale Spaces for Fiber Enhancement in DW-MRI
Journal of Mathematical Imaging and Vision
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In order to describe anisotropy in image processing models or physical measurements, matrix fields are a suitable choice. In diffusion tensor magnetic resonance imaging (DT-MRI), for example, information about the diffusive properties of water molecules is captured in symmetric positive definite matrices. The corresponding matrix field reflects the structure of the tissue under examination. Recently, morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images have been extended to matrix-valued data. In this article we consider an adaptive, PDE-driven dilation process for matrix fields. The anisotropic morphological evolution is steered with a matrix constructed from a structure tensor for matrix valued data. An important novel ingredient is a directional variant of the matrix-valued Rouy-Tourin scheme that enables our method to complete or enhance anisotropic structures effectively. Experiments with synthetic and real-world data substantiate the gap-closing and line-completing properties of the proposed method.