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The choice of local optimisation method used here is not critical,
except that it must be efficient. Furthermore, since it will be used
in a multi-resolution framework, the low resolution stages do not need
to find highly accurate transformations. Therefore the initial
parameter bracketing and the parameter tolerances (the size of
uncertainty on the optimised parameter values) are both made
proportional to the scale size. This avoids many unnecessary cost
function evaluations at low resolutions.
We initially chose Powell's method [15] as our local optimisation
method as it was efficient and did not require gradients to be calculated
which are especially difficult given the apodizations applied to the
cost functions. However, we discovered that a set of
1D golden searches [15] gave equally good results, which can be
reasonably expected if the parameterisation is close to decoupled.
Peter Bannister
2002-05-03