J. Weickert,
Recursive separable schemes for nonlinear diffusion filters,
B. ter Haar Romeny, L. Florack, J. Koenderink, M. Viergever (Eds.),
Scale-Space Theory in Computer Vision, Lecture Notes in Comp.
Science, Vol. 1252, Springer, Berlin, 260-271, 1997.
Poor efficiency is a typical problem of nonlinear diffusion
filtering, when the simple and popular explicit (Euler-forward)
scheme is used: for stability reasons very small
time step sizes are necessary.
In order to overcome this shortcoming, a novel type
of semi-implicit schemes is studied, so-called additive operator
splitting (AOS) methods. They share the advantages of explicit
and (semi-)implicit schemes by combining simplicity with absolute
stability. They are reliable, since they satisfy recently
established criteria for discrete nonlinear diffusion scale-spaces.
Their efficiency is due to the fact that they can be separated into
one-dimensional processes, for which a fast recursive algorithm with
linear complexity is available. AOS schemes reveal good rotational
invariance and they are symmetric with respect to all axes. Examples
demonstrate that, under typical accuracy requirements, they are at
least ten times more efficient than explicit schemes.
The full paper is available
online as well.
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