Staircasing in semidiscrete stabilised inverse linear diffusion algorithms

Authors:
M. Breuí;M. Welk
Affiliations:
Mathematical Image Analysis Group, Saarland University, Bld. E 1 1, 66041 Saarbrücken, Germany;Mathematical Image Analysis Group, Saarland University, Bld. E 1 1, 66041 Saarbrücken, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 11
Cited 5

Scale-Space and Edge Detection Using Anisotropic Diffusion

IEEE Transactions on Pattern Analysis and Machine Intelligence
A multi-scale approach to nonuniform diffusion

CVGIP: Image Understanding
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions

Mathematics of Computation
Scale Space Analysis by Stabilized Inverse Diffusion Equations

SCALE-SPACE '97 Proceedings of the First International Conference on Scale-Space Theory in Computer Vision
Total variation image restoration: numerical methods and extensions

ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
On the Equivalence of Soft Wavelet Shrinkage, Total Variation Diffusion, Total Variation Regularization, and SIDEs

SIAM Journal on Numerical Analysis
Weakly Constrained Minimization: Application to the Estimation of Images and Signals Involving Constant Regions

Journal of Mathematical Imaging and Vision
Neighborhood filters and PDE’s

Numerische Mathematik
Theoretical foundations for spatially discrete 1-D shock filtering

Image and Vision Computing
Image segmentation and edge enhancement with stabilized inverse diffusion equations

IEEE Transactions on Image Processing
Forward-and-backward diffusion processes for adaptive image enhancement and denoising

IEEE Transactions on Image Processing

Theoretical Foundations for Discrete Forward-and-Backward Diffusion Filtering

SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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
Anti-diffusion method for interface steepening in two-phase incompressible flow

Journal of Computational Physics
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

Quantified Score

Hi-index	7.30

Visualization

Abstract

We consider a semidiscrete model problem for the approximation of stabilised inverse linear diffusion processes. The work is motivated by an important observation on fully discrete schemes concerning the so-called staircasing phenomenon: when sharpening monotone data profiles, fully discrete methods generally introduce stepfunction-type solutions reminiscent of staircases. In this work, we show by an analysis of dynamical systems in corresponding semidiscrete formulations that already the semidiscrete numerical model contains the relevant information on the occurrence of staircasing. Numerical experiments confirm and complement the theoretical results.