Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
Introduction to “Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works”
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Geometric shock-capturing eno schemes for subpixel interpolation, computation and curve evolution
Graphical Models and Image Processing
Mathematical Morphology and Its Applications to Image and Signal Processing
Mathematical Morphology and Its Applications to Image and Signal Processing
Flux correction tools for finite elements
Journal of Computational Physics
Morphological Image Analysis: Principles and Applications
Morphological Image Analysis: Principles and Applications
Mathematical Morphology: 40 Years On : Proceedings of the 7th International Symposium on Mathematical Morphology, April 18-20, 2005 (Computational Imaging and Vision)
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Stabilised nonlinear inverse diffusion for approximating hyperbolic PDEs
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Anisotropic Continuous-Scale Morphology
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
Highly Accurate PDE-Based Morphology for General Structuring Elements
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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
Numerical invariantization for morphological PDE schemes
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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
Novel schemes for hyperbolic PDEs using osmosis filters from visual computing
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
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Dilation and erosion are the fundamental operations in morphological image processing. Algorithms that exploit the formulation of these processes in terms of partial differential equations offer advantages for non-digitally scalable structuring elements and allow sub-pixel accuracy. However, the widely-used schemes from the literature suffer from significant blurring at discontinuities. We address this problem by developing a novel, flux corrected transport (FCT) type algorithm for morphological dilation/erosion with a flat disc. It uses the viscosity form of an upwind scheme in order to quantify the undesired diffusive effects. In a subsequent corrector step we compensate for these artifacts by means of a stabilised inverse diffusion process that requires a specific nonlinear multidimensional formulation. We prove a discrete maximum---minimum principle in this multidimensional framework. Our experiments show that the method gives a very sharp resolution of moving fronts, and it approximates rotation invariance very well.