Name
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/978-3-642-15986-2_54 | DAGM-Symposium |
Keywords | Field | DocType |
anisotropic diffusion filter,simple explicit scheme,fed scheme,linear diffusion problem,latter case fed scheme,diffusion tensor,explicit scheme,so-called fast explicit diffusion,explicit finite difference scheme,explicit schemeswith varying time,linear system,anisotropic diffusion,steady state,image compression | Anisotropic diffusion,Applied mathematics,Mathematical optimization,Embedding,Linear system,Finite difference,Filter (signal processing),Steady state,Image compression,Mathematics,Parabola | Conference |
Volume | ISSN | ISBN |
6376 | 0302-9743 | 3-642-15985-0 |
Citations | PageRank | References |
34 | 1.42 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Sven Grewenig | 1 | 113 | 5.94 |
| Joachim Weickert | 2 | 5489 | 391.03 |
| Andrés Bruhn | 3 | 1558 | 82.42 |