J. Weickert,
Efficient image segmentation using partial differential equations and
morphology,
Report 3/2000, Computer Science Series, Dept. of Mathematics and
Computer Science, University of Mannheim, 68131 Mannheim, Germany,
February 2000.
(Revision of Technical Report DIKU-98/10, Dept. of Computer Science,
University of Copenhagen, Denmark, 1998.)
The goal of this paper is to investigate segmentation methods
that combine fast preprocessing algorithms using partial differential
equations (PDEs) with a watershed transformation with region
merging.
We consider two well-founded PDE methods: a nonlinear isotropic
diffusion filter that permits edge enhancement,
and a convex nonquadratic variational image restoration method
which gives good denoising.
For the diffusion filter, an efficient algorithm is applied
using an additive operator splitting (AOS) that leads to recursive
and separable filters. For the variational restoration method,
a novel algorithm is developed that uses AOS schemes within a
Gaussian pyramid decomposition.
Examples demonstrate that preprocessing by these PDE techniques
significantly improves the watershed segmentation, and that the
resulting segmentation method gives better results than some
traditional techniques.
The algorithm has linear complexity and it can be used for
arbitrary dimensional data sets. The typical CPU time for segmenting
a 256 x 256 image on a modern PC is far below one second.
The
full paper is available online as well.
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