Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image selective smoothing and edge detection by nonlinear diffusion
SIAM Journal on Numerical Analysis
A general framework for low level vision
IEEE Transactions on Image Processing
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Iterative Parameter-Choice and Multigrid Methods for Anisotropic Diffusion Denoising
SIAM Journal on Scientific Computing
Hierarchical tree of image derived by diffusion filtering
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
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Efficient numerical schemes for nonlinear diffusion filtering based on additive operator splitting (AOS) were introduced in [10]. AOS schemes are efficient and unconditionally stable, yet their accuracy is low. Future applications of nonlinear diffusion filtering may require additional accuracy at the expense of a relatively modest cost in computations and complexity.To investigate the effect of higher accuracy schemes, we first examine the Crank-Nicolson and DuFort-Frankel second-order schemes in one dimension. We then extend the AOS schemes to take advantage of the higher accuracy that is achieved in one dimension, by using symmetric multiplicative splittings. Quantitative comparisons are performed for small and large time steps, as well as visual examination of images to find out whether the improvement in accuracy is noticeable.