J. Weickert, B.M. ter Haar Romeny, M.A. Viergever,
Conservative image transformations with restoration and
scale-space properties,
Proc. 1996 IEEE International Conference on Image Processing
(ICIP-96, Lausanne, Sept. 16-19, 1996), Vol. 1, 465-468,
1996.
Many image processing applications require to solve problems such as
denoising with edge enhancement, preprocessing for segmentation, or
the completion of interrupted lines. This may be accomplished
by applying a suitable nonlinear anisotropic diffusion process to the
image. Its diffusion tensor is adapted to the differential structure of
the underlying image. Although being image enhancement tools, filters
of this class are well-posed.
The temporal evolution of the diffusion process creates a scale-space
whose causality properties can be understood in a deterministic,
stochastic, information theory based and Fourier based way.
The well-posedness and scale-space results carry over to the discrete
setting, which gives rise to reliable algorithms preserving all
properties of the continuous framework.
The full paper is available
online as well.
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