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Experimental Validation and Application

The overlap-based and model-based approaches were validated and compared, using a dataset consisting of 36 transaxial mid-brain slices, extracted at equivalent levels from a set of T1-weighted 3D MR scans of different subjects. Eight manually annotated anatomical labels were used as the basis for the overlap method: L/R white matter, L/R grey matter, L/R lateral ventricle, and L/R caudate. The images were brought into alignment using an NRR algorithm based on MDL optimisation [18]. The resulting appearance model is shown in Figure 6. A test set of different mis-registrations was then created by applying smooth pseudo-random spatial warps to the registered images. These warps were based on biharmonic Clamped Plate Splines. Each warp was controlled by 25 randomly placed knot-points, each displaced in a random direction by a distance drawn from a Gaussian distribution whose mean controlled the average magnitude of pixel displacement over the whole image. Ten different warp instantiations were generated for each image at each of seven progressively increasing values of average pixel displacement. Registration quality was measured, for each level of registration degradation, using several variants of each of the proposed assessment methods.

Figure 2: The calculation of a shuffle difference image

Figure: Shuffle difference images between the images on the extreme left and right for $r = 1\:\mbox{(abs. diff.)},\:1.5,\: 2.1 \mbox{ \& } 3.7$ from left to right.

To illustrate practical application of the method, we use the brain images described above, and compare the results of three different registration algorithms: a pairwise registration of each training set image to a fixed reference image chosen from the training set, and two MDL groupwise methods, as described above, one with no explicit constraints on the spatial deformations during the registration process (Groupwise 1) and a second which uses a statistical shape model to constrain the allowed spatial deformations between the images during registration (Groupwise 2)  [18].

Figure 4: From Left: Specificity ($S$), Generalisation ($G$) & Tanimoto overlap ($\mathcal{O}$) as a function of misregistration.