Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
SIAM Journal on Numerical Analysis
Image Compression with Anisotropic Diffusion
Journal of Mathematical Imaging and Vision
Efficient and reliable schemes for nonlinear diffusion filtering
IEEE Transactions on Image Processing
Domain transform for edge-aware image and video processing
ACM SIGGRAPH 2011 papers
Fast PDE-Based image analysis in your pocket
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Fast explicit diffusion for registration with direction-dependent regularization
WBIR'12 Proceedings of the 5th international conference on Biomedical Image Registration
ECCV'10 Proceedings of the 11th European conference on Trends and Topics in Computer Vision - Volume Part II
A cyclic projected gradient method
Computational Optimization and Applications
Approximate inference for spatial functional data on massively parallel processors
Computational Statistics & Data Analysis
Sparse Non-negative Stencils for Anisotropic Diffusion
Journal of Mathematical Imaging and Vision
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There are two popular ways to implement anisotropic diffusion filters with a diffusion tensor: Explicit finite difference schemes are simple but become inefficient due to severe time step size restrictions, while semi-implicit schemes are more efficient but require to solve large linear systems of equations. In our paper we present a novel class of algorithms that combine the advantages of both worlds: They are based on simple explicit schemes, while beingmore efficient than semi-implicit approaches. These so-called fast explicit diffusion (FED) schemes perform cycles of explicit schemeswith varying time step sizes that may violate the stability restriction in up to 50 percent of all cases. FED schemes can be motivated froma decomposition of box filters in terms of explicit schemes for linear diffusion problems. Experiments demonstrate the advantages of the FEDapproach for timedependent (parabolic) image enhancement problems as well as for steady state (elliptic) image compression tasks. In the latter case FED schemes are speeded up substantially by embedding them in a cascadic coarse-to-fine approach.