J. Weickert, B.M. ter Haar Romeny, M.A. Viergever,
Efficient and reliable schemes for nonlinear diffusion
filtering,
IEEE Trans. Image Processing, Vol. 7, 398-410, 1998.
Nonlinear diffusion filtering 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 recent 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.
The full paper is available
online as well.
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