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New methods and extensions of existing ones soon began to emerge. As part of an evaluation of many techniques, with the aim of justifying the use of model-based functions, new ones were created with some logical backing. The majority of these are detailed below.
There have been several attempts to properly register data by creating models of the reference and each image in the set in turn. This is an interesting idea to look at because, in principle, models can be proven to be good pair-wise measures as well.
Such functions describe the volume of data distributions. More uniform data, as one aspires to achieve across all images during registration, will result in lower such values. An exponential PDF was used in the experiments by default although over a dozen others are available in AART, including a Gaussian one. In line with Cootes' implementation for the ECCV 2004 paper [], this PDF-based function was created and used amongst the different objective functions under evaluation.
A personal suggestion was to use wavelets [] as indicator of data complexity. It was inspired by Twining's mentioning of Fourier transforms. As compression is closely related to MDL, these can provide an accurate estimate of the complexity of data and abundance of patterns within that data. An extensive group of different wavelets are offered by the application and, by default, Daubechy was used in the experiments. Computationally cheaper alternatives to the wavelets are Fourier and Hough transforms, but these have not yet been incorporated into AART. All wavelet implementations were supplied by the MATLAB Wavelet Toolbox.
This strand of methods [,] will analyse the peaks of image histograms. Normalised MI is currently one of the most robust and widely-used methods for 2-D data.
Much earlier in the year, a combination of objective functions was investigated, mainly that of MSD and model-based. One such hybrid method performed an MSD-driven routine, followed by a model-based one. Under such approach, it is assumed that the model-based objective function is well-behaved near convergence. Other schemes combined and altered between MSD- and a model-based objective function every fixed number of iterations (the algorithms were operated in alternating cycles).