Registration is an important component in many medical image analysis applications. It is used in motion correction, multi-modal fusion, mapping to Talairach space and many other tasks. Furthermore, when analysing large quantities of data, such as in a clinical study or within a busy imaging unit, it is desirable to have fully automatic registration methods. Such methods offer reliability and repeatability as well as minimising user interaction.
A standard method of solving the registration problem is to treat it as a mathematical optimisation, using a cost (or similarity) function to quantify the quality of the alignment of the two images for any given transformation. In practice, this formulation relies on the use of a global optimisation method. This optimisation method is crucial for obtaining good registrations. However, to date most attention has been focused on other aspects of the problem, such as defining cost functions, rather than on the optimisation method.
Most of the mathematical optimisation methods that exist are only suitable for local optimisation and therefore will not find the global solution in general. These methods include gradient descent, Powell's method, simplex methods and so on [Press et al., 1995]. Furthermore, the global optimisation methods that do exist often require a very large number of iterations to satisfy convergence criteria [Geman and Geman, 1984,Ingber, 1989], which is impractical for volumetric registration where evaluating the cost function for many values of registration parameters is particularly time consuming.
In an attempt to solve the global optimisation problem in a reasonable amount of time, many registration methods rely on a multi-resolution approach. This is hoped to enable local optimisation methods to reach the global minimum. The assumption is that it is easier to find the global minimum when using large sub-sampling, since coarser transformation steps can be taken, which should reduce the chance of there being a local minimum between the initial starting position and the global minimum. This global minimum is then tracked across different resolutions by successive local optimisations at a series of sub-samplings.
This report examines the assumptions underlying the registration problem (sections 2 and 3) and shows that the use of local optimisation methods together with the standard multi-resolution approach is not sufficient to reliably find the global minimum. In addition, a global optimisation method is proposed (section 4) that is specifically tailored to this registration problem, together with a full discussion of all the necessary implementation details (section 5). Finally, results are presented (section 6) that show that the proposed method is more reliable at finding the global minimum than several of the currently available registration packages in common usage.