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3 Problem Definition
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Improving model shape acquisition
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1 Introduction
The integration of geometric constraints into the shape fitting process
has been treated for wire frame model construction by Porrill [
8
]. Wire frame models were constructed from stereo-data. The model
features were given statistical distributions and geometric constraints
between features produced dependencies in the distributions. The model
adjustment process maximized the
a posteriori
probability of the models. Since the models were based on wire frames,
the constraints were related to lines. Four types of constraints were
considered: orthogonality, intersection, equality and connection by a
small rigid motion. The optimal feature parameters were estimated using
an extended Kalman filter. At each iteration, constraints are linearized
in the neighborhood of the current estimate, and then used to correct
the measurement. Porrill's approach is nice since it takes advantage of
the recursive linear estimation of Kalman filtering, however it assumes
a Gaussian distribution which may not always the case. Moreover, the
method, guarantees the satisfaction of the constraints only to
linearized first order. Additional iterations at each estimation step
are needed if one would like to obtain more accuracy. This last
condition has been taken into account in the work of De Geeter and al [
4
] by defining a ``Smoothly Constrained Kalman Filter''. The key of their
approach is to replace a nonlinear constraint by a set of linear
constraints applied iteratively and updated by new measurements in order
to reduce the linearization error.
Naoufel Werghi
Thu Jul 10 17:36:04 BST 1997