International Journal of Computer Vision
Geometric shock-capturing eno schemes for subpixel interpolation, computation and curve evolution
Graphical Models and Image Processing
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
Numerical Solution Schemes for Continuous-Scale Morphology
SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion
Journal of Mathematical Imaging and Vision
Staircasing in semidiscrete stabilised inverse linear diffusion algorithms
Journal of Computational and Applied Mathematics
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
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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The two fundamental operations in morphological image processing are dilation and erosion. These processes are defined via structuring elements. It is of practical interest to consider a variety of structuring element shapes. The realisation of dilation/erosion for convex structuring elements by use of partial differential equations (PDEs) allows for digital scalability and subpixel accuracy. However, numerical schemes suffer from blur by dissipative artifacts. In our paper we present a family of so-called flux-corrected transport (FCT) schemes that addresses this problem for arbitrary convex structuring elements. The main characteristics of the FCT-schemes are: (i) They keep edges very sharp during the morphological evolution process, and (ii) they feature a high degree of rotational invariance. We validate the FCT-scheme theoretically by proving consistency and stability. Numerical experiments with diamonds and ellipses as structuring elements show that FCT-schemes are superior to standard schemes in the field of PDE-based morphology.