Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
International Journal of Computer Vision
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
International Journal of Computer Vision
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Computer and Robot Vision
The Morphological Structure of Images: The Differential Equations of Morphological Scale-Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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
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The partial Differential equations describing the propagation of (wave) fronts in space are closely connected with the morphological erosion and dilation. Strangely enough this connection has not been explored in the derivation of numerical schemes to solve the Differential equations. In this paper the morphological facet model is introduced in which an analytical function is locally fitted to the data. This function is then dilated analytically with an infinitesimal small structuring element. These sub-pixel dilationsform the core of the numerical solution schemes presented in this paper. One of the simpler morphological facet models leads to a numerical scheme that is identical with a well known classical upwind finite Difference scheme. Experiments show that the morphological facet model provides stable numerical solution schemes for these partial Differential equations.