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... set1.1
In this thesis, ``texture'' is used in the graphics sense to mean the intensity pattern. 
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... scaling2.1
The exclusion of scaling makes this a rigid transformation, rather than Euclidean transformation. 
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...2.2
Other transformations such as taper, on the contrary, are not parallelism preserving. The importance of this rigorous constraint is that the distance between any two points remains proportional to the transformation. 
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... effect2.3
A pixel of course can be mapped onto the exact same original position, but the idea is that a continuous flow should remain. 
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... method2.4
The discovery of mutual information is also attributed to Maes, yet some argue that the work was sparked by Viola in the mid-nineties. It is now accepted that Collignon et al, and Viola and Wells, came up with the idea of mutual information for registration independently and at about the same time. Collignon, Maes et al. published in 1995, and Viola also published in 1995. 
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... process2.5
There is an additional distinction between symmetric and asymmetric normalised mutual information, but rationale for this requires the full technical recipe. The dissertation at http://www.lans.ece.utexas.edu/~strehl/diss/node107.html summarises the way in which NMI is evaluated. 
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...2.6
In the case of cortical surface registration, surface-to-surface registration is worthy of consideration []. These ideas can be applied to cortical hemispheres, LDDMM-Curve being a recent example []. Auzias et al. [] have sulci automatically identified and Joshia et al. [] register cortical surfaces using labeled sulcal curves. 
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... for3.1
A sensible choice might be, for example, 98% of the observed variation, which means that 2% of the variation is not accounted for. In practice, that 2% of the overall variation is usually the least informative and it is possibly made up from noise and error. Annulling this effect is, among other things, what PCA is intended to accomplish. 
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...3.2
There are different possible colour schemes [], but they need not have any effect on principles of sampling intensities. 
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... shape3.3
Warps can be applied using a strategy borrowed from graphics. In all experiments described in this thesis this was achieved by a triangulated mesh generated from the landmark points and barycentric coordinates to mesh the intersections put in vector $\mathbf{g}$ (Equation 3.3). 
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...3.4
The letter $s$ stands for shape, as by default this matrix scales the shape parameters only. It gives logically equivalent results to these of applying the factor $\mathbf{W}_{g}=\frac{1}{\mathbf{W}_{s}}$ to intensities. 
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... differences3.5
A simple measure of difference is used here although this need not necessarily be the case. 
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... matrix3.6
The matrix $\mathbf{A}$ can be obtained using linear regression. 
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... lie3.7
Advanced knowledge about the problem is highly conductive at this stage. Otherwise, a bottom-up image analysis is a must. 
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... off-line3.8
If these correlations are not available, guessing would be an alternative. It is important, however, to learn from the experience gained during this independent run of the program or else the optimisation would behave senselessly and lead to improvements being identified very slowly. General optimisers are assumed to make a good judgment as such. 
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...4.1
It is not a complicated idea, yet a very fundamental one which was first introduced in 1948. 
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...4.2
MDL, as described by Rissanen, provides a measure of the minimal amount of information necessary to encode some data and any data can be transformed in a particular way so that it becomes a sequence of symbols (e.g. numbers, strings, signals). 
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... bumps5.1
It should be emphasised that bumps are - at least in this context - merely 1-D images, or vectors. 
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... boundaries5.2
In principle, thin-plate splines or B-splines could also be used provided there are constraints to prevent folding or tearing. 
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... regions5.3
Particularly in the bio-medical domain, visibility of all constituent structures becomes crucial. 
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... diffeomorphic5.4
While the bump may have its form tweaked and manipulated, its highest peak should be preserved although it may move leftward or rightward. This assumes that boundaries for the warp intensity are not affected. 
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... closest5.5
Proximity is calculated based on the Euclidean distance, which identifies the reference that is, on average, nearest to all other images. 
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... image5.6
The reference must remain static in this case. 
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...5.7
I changed parameter values dynamically, depending on the progress of the algorithm. 
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... scales5.8
Coarser images were registered first in order to obtain a good initial approximation for the warps used towards the end, when finer-level images were registered. 
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