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General optimisation is often used in the process of matching and its complexity can be relatively high. The behaviour of such a problem is not linear and it may cross over to the realms of quadratic programming (QP) where various parameters simultaneously control a function and minimisation is therefore by no means trivial. This process is by convention concerned with the minimisation (complement is used to generalise to maximisation) of the value of a function and that function often comprises more than a single variables which makes it multi-dimensional. Many software products that act as general optimisers exist and the way they operate and perform varies. Some even switch between different algorithms depending on the stage of the optimisation and the changing granularity of the problem.
Optimisation over a function which varies in many dimensions is an expensive process. Often this optimisation shall require some a priori knowledge of the problem domain so that performance winds up being satisfactory. In the case of image matching, advantages can be gained if the effect of variable alteration can be predicted in some way. An example of this was described in Subsection 2.5 where pixel intensities have a dependency upon a group of parameters. Slightly less specifically, given the difference between two or more images, or even some generic data regarding a change caused by value changes in the function considered for optimisation, it should then be possible to determine paths that lead to quick convergence.
For the problems outlined in the document, common optimisation methods are gradient-descent and downhill simplex. However, many other methods exist34 and whole books have been written on the subject [38]. The advocated strategy would sometimes be a utilisation of mixtures of different methods with rational choice of the most relevant one at each stage. That is plainly because the different characteristics of the methods make them advantageous at different states throughout the entire optimisation process.