Images, numerical analysis of singularities and shock filters
Images, numerical analysis of singularities and shock filters
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Signal and image restoration using shock filters and anisotropic diffusion
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
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
Mathematics of Computation
SIAM Journal on Scientific 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
A Shock-Capturing Algorithm for the Differential Equations of Dilation and Erosion
Journal of Mathematical Imaging and 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
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Stabilised backward diffusion processes have shown their use for a number of image enhancement tasks. The goal of this paper is to show that they are also highly useful for designing shock capturing numerical schemes for hyperbolic conservation laws. We propose and investigate a novel flux corrected transport (FCT) type algorithm. It is composed of an advection step capturing the flow dynamics, and a stabilised nonlinear backward diffusion step in order to improve the resolution properties of the scheme. In contrast to classical FCT procedures, we base our method on an analysis of the discrete viscosity form. This analysis shows that nonlinear backward diffusion is necessary. We employ a slope limiting type approach where the antidiffusive flux determined by the viscosity form is controlled by a limiter that prohibits oscillations. Numerical experiments confirm the high accuracy and shock capturing properties of the resulting scheme. This shows the fruitful interaction of PDE-based image processing ideas and numerical analysis.