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A comparison between most of the methods was conducted and the conditions were set to be impartial and well-scaled so that they evaluate a proper registration process.
For the results in Table ![[*]](/IMG/latex/crossref.png)
, the number
of iterations was set to 50. By another terminology7.13, this equates to 1000 as each of the twenty data instances was subjected
to up to 50 transformations. For single-point transformations, the
placement of the control point was random (both in location and magnitude)
and for multi-point transformations the positioning of points was
made random to abstain from data-bias or advantageous a priori
knowledge. The number of data instances was kept high at 20 in order
to allow a substantial group-wise optimisation to be investigated.
Objective functions based on mutual information remained flat simply
due to the continuity of the data and the fact that it is one-dimensional.
The table below shows the different values of
.
are the Eigen-values derived from the covariance matrix of the appearance model which had been constructed from all 20 data instances7.14. For completeness, differentiation is provided for optimisations which reparameterise over all dimensions at once (joint) or do so separately (sequential).
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