From adaptive averaging to accelerated nonlinear diffusion filtering

Authors:
Stephan Didas;Joachim Weickert
Affiliations:
Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany;Mathematical Image Analysis Group, Faculty of Mathematics and Computer Science, Saarland University, Saarbrücken, Germany
Venue:
DAGM'06 Proceedings of the 28th conference on Pattern Recognition
Year:
2006

Citing 7
Cited 2

Scale-Space and Edge Detection Using Anisotropic Diffusion

IEEE Transactions on Pattern Analysis and Machine Intelligence
Adaptive Smoothing: A General Tool for Early Vision

IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion

SIAM Journal on Numerical Analysis
SUSAN—A New Approach to Low Level Image Processing

International Journal of Computer Vision
A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing, and the Nonlinear Diffusion Equation

IEEE Transactions on Pattern Analysis and Machine Intelligence
Bilateral Filtering for Gray and Color Images

ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
On the origin of the bilateral filter and ways to improve it

IEEE Transactions on Image Processing

Combining curvature motion and edge-preserving denoising

SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Generalised Nonlocal Image Smoothing

International Journal of Computer Vision

Quantified Score

Hi-index	0.00

Visualization

Abstract

Weighted averaging filters and nonlinear partial differential equations (PDEs) are two popular concepts for discontinuity-preserving denoising. In this paper we investigate novel relations between these filter classes: We deduce new PDEs as the scaling limit of the spatial step size of discrete weighted averaging methods. In the one-dimensional setting, a simple weighted averaging of both neighbouring pixels leads to a modified Perona-Malik-type PDE with an additional acceleration factor that provides sharper edges. A similar approach in the two-dimensional setting yields PDEs that lack rotation invariance. This explains a typical shortcoming of many averaging filters in 2-D. We propose a modification leading to a novel, anisotropic PDE that is invariant under rotations. By means of the example of the bilateral filter, we show that involving a larger number of neighbouring pixels improves rotational invariance in a natural way and leads to the same PDE formulation. Numerical examples are presented that illustrate the usefulness of these processes.