6 CONCLUSIONS
We introduced a closed form conditional likelihood
function for errors-in-variables problems. It only de-
pends on the parameters of interest, in contrast to
the equivalent likelihood functions as introduced by
Gleser (Gleser, 1981) containing nuisance parame-
ters. Well known estimation schemes known from
literature (Nagel, 1995; Kanatani, 2008; Leedan and
Meer, 2000; Chojnacki et al., 2001; Matei and Meer,
2006) turned out to be special cases of our condi-
tional ML estimator for mutually independent obser-
vations. Therefore error bounds for these estimators
can be calculated as done here. In addition our ap-
proach covers also the case of arbitrary correlations
between measurements.
A straight forward extension of the algorithm from
(Matei and Meer, 2006) iterating SVDs (i.e. Type I )
turned out to have oscillating convergence behavior
when correlated noise is modeled. We did not ob-
serve such behavior for our novel algorithm (i.e. Type
II ). In addition, we experimentally showed for an op-
tical ﬂow application the beneﬁts of having a likeli-
hood function at hand as the likelihood approach dis-
tinguishes good estimates from less reliable estimates.
In such detected, well-structured image regions our
simple local approach even performs better than an
optical ﬂow algorithm with regularization (Sun et al.,
2010) currently among the better performing ones on
the Middlebury test set (Baker et al., 2007). We con-
clude that using a non-regularized estimator can in-
deed be beneﬁcial, when not interested in the whole
image, but the ’good data’ regions. Further we con-
clude that driving regularization by estimated CRLB
may be beneﬁcial and is to be investigated in future
research.
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