Highly Accurate PDE-Based Morphology for General Structuring Elements

Authors:
Michael Breuß;Joachim Weickert
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany 66041;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany 66041
Venue:
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Year:
2009

Citing 9
Cited 1

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
Geometric shock-capturing eno schemes for subpixel interpolation, computation and curve evolution

Graphical Models and Image Processing
Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing

ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Numerical Solution Schemes for Continuous-Scale Morphology

SCALE-SPACE '99 Proceedings of the Second International Conference on Scale-Space Theories in Computer Vision
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)

Mathematical Morphology: 40 Years On : Proceedings of the 7th International Symposium on Mathematical Morphology, April 18-20, 2005 (Computational Imaging and 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 Schemes for PDE-Based Morphology with General Convex Structuring Elements

International Journal of Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

Modelling the morphological processes of dilation and erosion with convex structuring elements with 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 rotational invariance. 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.