Workshop on Bioimaging II / PDEs, Thu, 22 Nov, 2007
Speaker: Martin Rumpf
Abstract
The estimation of motion in an image sequence is a fundamental task in image processing.
Frequently, the image sequence is corrupted by noise and one simultaneously asks for a restored
sequence and the underlying motion field. In smoothly shaded regions of the restored image sequence
the brightness constancy assumption along motion paths leads to a pointwise differential condition on the motion field.
At object boundaries which are edge discontinuities both for the image intensity and the motion field this condition is no longer
well-defined. In this paper a total variation type functional is discussed for the joint image restoration and motion estimation.
This functionals appears to be not lower semicontinuous. By the general theory on vector valued
BV functionals its relaxation comes along with a singular part of the energy density which is given by the solution
of a local minimization problem at edges. In the case of one space dimension this energy density can be identified explicitly.
This relaxation leads to a generalized variational formulation of the brightness constancy assumption.
Furthermore, it enables to resolve an ambiguity problem in the selection of foreground and background motion
In case of fast motion a minimization of the functional favors microstructures at object boundaries, which
can be avoided by a suitable scaling of the model.
This is joint work with Sergio Conti from Duisburg-Essen University.
URL: www.ricam.oeaw.ac.at/specsem/ssqbm/participants/abstracts/index.php
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