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1983 ) is used. A possible extension of our optimisation technique not regarded in
the experiments described in Sect. 5.1.3 is to first weight down errors with a robust
estimator, and if after some iteration steps some points are regarded as outliers, to
repeat the weighting on the reduced set of observations. Furthermore, it might be
favourable to compare the residuals with their individual covariance information,
which provides information about how much larger a residual is than it is thought
to be determined from the given data. Such techniques are known to improve the
convergence behaviour in many applications, but in the experiments regarded in
Sect. 4 our simple robust estimator was always sufficient to obtain a solution after a
few tens of iterations of the Levenberg-Marquardt scheme.
5.1.2 Online Version of the Algorithm
The integrated three-dimensional reconstruction method described so far is an of-
fline algorithm. The error term ( 5.1 ) is minimised once for the complete image se-
quence after acquisition. This section describes an online version of the proposed
combination of structure from motion and depth from defocus as presented by Wöh-
ler et al. ( 2009 ), processing the acquired images instantaneously and thus generating
a refined reconstruction result as soon as a new image has been acquired. This is a
desired property for systems, e.g. in the context of mobile robot navigation, simul-
taneous localisation and mapping (SLAM), or in situ exploration.
The online version starts by acquiring the current image. Features already present
in the previous image are searched by the KLT tracker, and lost features may be re-
placed with new ones. The amount of defocus is obtained for each feature within the
current frame based on the high-frequency integral H of the ROI around the feature
position (cf. ( 4.17 )). For each tracked feature, the best focused ROI is determined by
fitting a second-degree polynomial to the values of H . Possible candidates that may
already have passed their point of best focus are identified based on a threshold rat-
ing. The initial depth value is then computed for each tracked feature by estimating
the PSF radius σ as outlined in Sect. 4.2.3.2 .
The depth values obtained by the depth from defocus method are used to ini-
tialise the Levenberg-Marquardt scheme, which determines the camera transforms
and three-dimensional feature points that minimise the error function given by ( 5.1 )
using an M-estimator as in the offline version. The current optimisation result is
used as an initialisation to the subsequent iteration step involving the next acquired
image.
5.1.3 Experimental Evaluation Based on Tabletop Scenes
In the tabletop experiments a Baumer industrial CCD camera with an image size of
1032
×
776 pixels, equipped with a Cosmicar-Pentax video lens of 12 mm focal
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