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Optimisation

An optimisation strategy is needed in order to identify parameterisations that lead to better models. Various methods were explored in the attempt to reach good solutions and reach them quickly. A general-purpose optimiser seems like the most natural choice to make, but it does not necessarily produce good results. Such an optimiser, for example, can be faced with the task of handling very large sets of shapes. This slows down the optimisation and makes it less effective.

One alternative approach to optimisation is to handle shapes in isolation. A one-at-a-time optimiser will have a single shape and reparameterisation to handle while all other shapes are unchanged. This simplifies the problem and works well in practice.

Another key method that handles high complexity and scale is a multi-resolution approach, which refers to the size of the kernels used in the reparameterisation. Gross estimates of a good solution can be found early on and then be propagated for use in optimisation over kernels at another scale. Davies et al. [] found that it helped in cases where data was cluttered. Random selection of reparameterisation proved useful too.

The process of optimisation in the case above involved a number of steps:

  1. Pick a shape
  2. Pick a fixed breadth and width for the kernel function that generates the re-parameterisation
  3. Optimise the objective function wrt kernel amplitude
  4. Repeat (back to (1), until the results are satisfactory)
There were variants to this method as well, which proved worthwhile. For example, picking several kernels before moving on to next shape is a strategy that led to improvements.

Roy Schestowitz 2010-04-05