Efficient and reliable schemes for nonlinear diffusion filtering
- 1 March 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Image Processing
- Vol. 7 (3) , 398-410
- https://doi.org/10.1109/83.661190
Abstract
Nonlinear diffusion filtering in image processing is usually performed with explicit schemes. They are only stable for very small time steps, which leads to poor efficiency and limits their practical use. Based on a discrete nonlinear diffusion scale-space framework we present semi-implicit schemes which are stable for all time steps. These novel schemes use an additive operator splitting (AOS), which guarantees equal treatment of all coordinate axes. They can be implemented easily in arbitrary dimensions, have good rotational invariance and reveal a computational complexity and memory requirement which is linear in the number of pixels. Examples demonstrate that, under typical accuracy requirements, AOS schemes are at least ten times more efficient than the widely used explicit schemes.Keywords
This publication has 33 references indexed in Scilit:
- A network for multiscale image segmentationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2003
- Linear Scale-Space Theory from Physical PrinciplesJournal of Mathematical Imaging and Vision, 1998
- Nonlinear Multiscale Representations for Image SegmentationComputer Vision and Image Understanding, 1997
- Regularization, Scale-Space, and Edge Detection FiltersJournal of Mathematical Imaging and Vision, 1997
- Images and PDE'sPublished by Springer Nature ,1996
- Local geometry variable conductance diffusion for post-reconstruction filteringIEEE Transactions on Nuclear Science, 1994
- Scale-space and edge detection using anisotropic diffusionPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1990
- Matrix TheoryPublished by Springer Nature ,1987
- Numerische Behandlung partieller DifferentialgleichungenPublished by Springer Nature ,1978
- A discrete analogue of the Weierstrass transformProceedings of the American Mathematical Society, 1960