next up previous
Next: Global Search Up: A Global-Local Hybrid Optimisation Previous: Multi-Resolution

Local Optimisation

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 $ N$ 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