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... object1
The word ``object'' will from here onwards refer to a structure of interest in $ n$-dimensional space. 
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... aperture2
In the case of medical imaging, there are even more factors to be considered, as opposed to a camera's aperture. 
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... rigid3
``Rigid'' refers to constrained variability and low model generalisability as explained later. It is significantly different from the term ``rigid'' in the context of registration. 
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... blow-up4
Current model-based methods typically deal with only the order of tens of thousands of pixels. High-resolution medical images can contain millions of pixels. 
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... image5
Edges and corners usually hold more information of use for subsequent analysis and aid segmentation. They lead to better identification of the different objects residing in the image. 
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... variation6
Offsets of standard deviation units from the mean of each mode then illustrate the effect each mode has. 
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... variation7
Because there is a total of $ n$ modes of variation, $ 1<s<n$, i.e. only $ n$ parameters exist. 
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... appearances8
One of the main aims and great power of appearance models is full synthesis so photo-realism is at a premium. 
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... for9
A common choice is 98% of the observed variation which means 2% of the variation is not accounted for. This 2% of variation is usually the least informative though which is the what PCA is intended to accomplish. 
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... pixel10
For colour it is common to use 24 bits and for grey-level just 8 bits. For more compact statistical appearance models, less than 8 bits (256 shades of grey) might suffice to achieve good results and in medical imaging 12 bits are nearly a standard in acquisition. 
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... image11
The distinction here is hard because the model can describe more than one valid independent object and usually represents only a partial section of the entire image. In a medical context, the term atlas fits somewhat more nicely and it usually describes a single organ or anatomical structure. 
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... set12
There is a subtlety which makes this phrasing a bit deceiving and inaccurate. The word ``range'' is a gross terminologically equivalent for the area that stretches in between the space of training set instances. It can be conceived as the space defined by a Gaussian distribution cloud that is deduced from the training set. 
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... model13
There are some more complex considerations as the model needs to be aligned properly as well as change form. 
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... intensity14
A simple raster scan that account for all pixels should clearly be fast under most contemporary computer architectures. This is indeed the case if simple operations like subtractions are pipelined on the ALU (arithmetic and logic unit). 
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... not15
The vector's distribution of values, i.e. positions with high absolute values, can answer this question quite coarsely. 
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... target16
This process of fitting strives to converge to the global minimum (of difference measure). Realistically speaking , the model and the target never reach complete equivalence, namely the difference value of 0. Even if the target was used to train the model, PCA would corrupt the connection between the two. 
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... lie17
Advanced knowledge about the problem is highly helpful at this stage, otherwise some bottom-up image analysis is a must. 
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... off-line18
If these are not available, some 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 very slowly. General optimisers ought to make a good judgement as such. 
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... lower19
Although results approve this claim, it is quite likely that better implementations and further improvements will suggest otherwise. 
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...20
The names infrequently change in the literature despite standardisation. What is important is the description of transformations and not the names or mnemonics that wound up describing them. 
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...21
Such a process is a very fundamental one in computer graphics modelling and various books cover shape-normalisation techniques and algorithms. 
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... values22
1 for scaling, 3 for x, y and z coordinates and 2 for rotation, e.g. the xy and yz angles $ \theta_{1}$and $ \theta_{2}$. 
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...23
Popular transformations such as skew, shear and 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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... structure24
A random uncontrollable transformation will dispart basic structures in the image and make interpretation impossible. 
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... Challenge25
The Grand Challenge aims to unify the different stages of analysis. It will be referred to yet again in Section 5 which deals with recent and on-going work. 
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... transformations26
This so-called mapping or transformation can be thought of as being a standard function, for example $ f(x,y)=(x',y')$ in 2-D and it is applied to all the pixels within a predefined range. 
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... image27
More generally, the functions are mappings defined over a matrix or a vector which is analogous to an image. 
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... effect28
A pixel of course can be mapped onto the exact same original position, but the idea is that a continuous flow must prevail. 
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... points29
A continuous function is independent of the number of points. Therefore, the complexity can be increased progressively to obtain finer, more accurate results. 
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... discussion30
In Manchester University, Cootes and others are in favour of many small warps, but some are in favour of few rather more complex warps that are controlled by a larger number of parameters. More details on such issues appear in later discussions on current work. 
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... way31
The discovery of this mutual information is actually attributed to Maes as well. The thesis worked on by Viola in the mid-nineties received great recognition though. 
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... literature32
There is an additional distinction between symmetric and asymmetric normalised mutual information, but explanation on 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 evaluated. 
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... sum33
One could suggest an extension to such a method and assign weights to differentiate regions of varying significance. 
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... exist34
To name several more methods: dynamic programming, genetic algorithms, Powell's, simulated annealing and steepest descent. 
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... search35
Exhaustivity is impossible for continuous functions, but digital images are luckily discrete. 
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... similarity36
It will temporarily be assumed that for an objective function that needs to be minimised, the similarity measure will return small values for good similarity and vice versa. 
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...37
Binary representation is quite complete in the sense that any data, e.g. programs and text, can be coded in a binary form. However, this representation might be very greedy of space and the issue of representation compactness then arises. 
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... correlation38
To make this appear more practical, one can think of a large ($ >100000$ pixels) image where patterns are present. 
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... these39
This can be portrayed as a uniform plain-white image. 
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... sequence40
General problem reducibility to a sequence is axiomatic as Turing Machines suggest. 
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... matrix41
This will indicate the volume of the model's scatter in space. The more compact a model appears, the lower this volume. 
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... involved42
Although knowledge of the problem is an integral part of most program optimisation steps, the more formal methods can be used to identify dependencies. A dependency graph can reliably indicate where re-evaluation is indeed necessary. 
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... interactive43
A reasonable response time depends on the purpose of the system, the level of detail, etc. 
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... data44
The data type is irrelevant. It makes no difference whether it is an image of full appearance or just a bump. 
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... search45
This similarity computation is incorporated in the objective function and it usually comprises a collection of pair-wise similarity measures. 
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... composite46
It will be prematurely assumed that the new synthetic data posses several distinct morphological attributes. 
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... choices47
Recent discussions also suggest that data may be similar to that used in Davies' thesis. 
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... issue48
Warps placement truly seems tactless and poor at present, but this needs to be confirmed by evidence. 
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... SNR49
The signal-to-noise ratio in medical images can be lower by orders of magnitude in comparison with visual images. 
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... aims50
Section 7 was bound to take a pessimistic point-of-view to describe worst-case scenarios. A more optimistic contemplation would have discussed the obtainable goals and the factors that make these goals hard to reach. 
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... productively51
Frequently it appears to be the case that in order to get reasonable results, high computational power is mandatory. In the absence of this power, experiments might fail or become impractical. 
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