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.)
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
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
A viscosity solutions approach to shape-from-shading
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
Coherence-Enhancing Diffusion Filtering
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
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
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Visualization and Processing of Tensor Fields (Mathematics and Visualization)
Image filtering using morphological amoebas
Image and Vision Computing
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
Image and Vision Computing
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
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
Adaptive Continuous-Scale Morphology for Matrix Fields
International Journal of Computer Vision
Morphological bilateral filtering and spatially-variant adaptive structuring functions
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
Morphological and Linear Scale Spaces for Fiber Enhancement in DW-MRI
Journal of Mathematical Imaging and Vision
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Matrix fields are important in many applications since they are the adequate means to describe anisotropic behaviour in image processing models and physical measurements. A prominent example is diffusion tensor magnetic resonance imaging (DT-MRI) which is a medical imaging technique useful for analysing the fibre structure in the brain. Recently, morphological partial differential equations (PDEs) for dilation and erosion known for grey scale images have been extended to three dimensional fields of symmetric positive definite matrices. In this article we propose a novel method to incorporate adaptivity into the matrix-valued, PDE-driven dilation process. The approach uses a structure tensor concept for matrix data to steer anisotropic morphological evolution in a way that enhances and completes line-like structures in matrix fields. Numerical experiments performed on synthetic and real-world data confirm the gap-closing and line-completing qualities of the proposed method.