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List of Figures

1. A target image $\mathbf{T}$ is being overlaid by a high-level representation (the model $\mathbf{M}$) which seeks to find a good fit.
2. Landmark identification and mark-up in medical imaging.
3. 3-D scatter of points.
4. Principal component in 2-D is indicated by the arrow.
5. Model and target fitting.
6. Registration examples; from top to bottom: rigid, affine and non-rigid transformations.
7. CPS non-rigid warp example. Warp is shown on the right-hand side.
8. Monotonically-increasing function.
9. Reparameterisation example. A point moves along the curve a distance $S'$ from the origin. All other points will do so as well to make this a continuous reparameterisation, often defined by a Cauchy.
10. Warp applied to image. On the left: image before warp is applied; On the right: image after warping.
11. Autonomous Appearance-based Registration Test-bed in February 2004.
12. Illustration of the three variation modes.
13. Data being registered. The registration process is visualised by an image composed of data vectors. The columns are 1-D vectors interpreted as grey-scale pixels.
14. Original data set of size 5 before any application of warps.
15. A larger example of pixel representation for 1-D bump data. This is somewhat of an enhancement to Figure cap:Data-being-registered..
16. Warps shown as the MSD objective function runs. Each row shows the reparameterisation which is applied to one of the 5 images in the same row.
17. Shape model of 10 data instances at the start. The four principal modes are shown with up to standard deviations away from the mean.
18. Intensity model of 10 data instances at the start. The two principal modes are shown with up to standard deviations away from the mean.
19. Combined (shape and intensity) model of 10 data instances at the start. The two principal modes are shown with up to standard deviations away from the mean.
20. Mean MSD measures at each point during the model-based registration of 10 data instances.
21. 2-D Synthetic data generated and evaluated for similarity against the reference.
22. Specificity rising when MSD-based registration is performed.
23. Specificity of model-based objective function.
24. Generalisation ability of model-based objective function.
25. Specificity of the model-based objective function as registration proceeds.
26. Generalisation ability of the model-based objective function as registration proceeds.
27. Specificity of the MSD objective function as registration proceeds.
28. Generalisation ability of the MSD objective function as registration proceeds.
29. Specificity shown to be less erratic as the algorithm proceeds with registration.
30. For MSD, generalisation slowly declines as shown for 2,000 iteration. Measurements are made every 100 iterations.
31. Specificity is merely unchanged as registration proceeds, unlike what is expected. It can be seen however, that there is a decline at the start where changes to the data are most radical.
32. Generalisation ability measured every 100 warps. A total number of 10,000 iterations shows no substantial change to values while registration is performed.
33. Multiple knot-point warps show that the curve is exponential when a model-based objective function is employed.
34. Various measures shown as the old model-based algorithm proceeds.
35. Data being visualised by AART. In this case, 5 bumps are shown at some arbitrary state during registration.
36. A comparative analysis of different objective functions. It illustrates that the model complexity decreases only for the newly-proposed objective functions. The Y-Axis value is an indicator of model compactness.
37. The old model-based objective function which gets stuck due to Ws inappropriately set.
38. Drops which illustrate the problems with optimisation.
39. Data alignment to discover correct solution. On the left: piece-wise linear warps to be applied to original data; on the right: data after alignment.
40. Evaluation going below target when initialised at the registration target. The target of registration is indicated by the straight horizontal line.
41. A long optimisation with the successful algorithm shows that it surpasses what is questionably the correct solution.
42. Highest peak being retained in registration.
43. The unregistered bump data and its three principal modes of variation (2 standard deviations).
44. graphical user interface for semi- automatic landmark selection as of June 2004.
45. Automatic precision and the differing rates of convergence for image registration.
46. Adaptive precision requirement resulting in different rates of convergence. This curve is drawn in the context of shapes and selection of landmark point.
47. A comparison of performances in landmark selection. Shown above is an algorithm which is based on an entire set versus one which is based on a stochastic subset. The latter is quicker and it fluctuates due to the varying selection of a subset (3 shapes out of 10 in total).
48. Schematic of the current registration algorithm. A reference image and the rest of the warped set form a combined model which is evaluated in an MDL-like manner.
49. Current algorithm at a lower level. The idea of a reparameterisation is shown by emphasising that images are formed by aggregation of the previous image with some parameterisation.
50. One possible proposal for the further development of the registration algorithm. The main idea to take is that residuals should drive warps that in turn affect the model.
51. A second reasonable proposal for algorithm extension. MDL is the main driver of warps here.
52. Down-sized poster.
53. Illustration of the approach taken when registering using subsets.
54. Images being registered according to the description length of the entire set of size 10. The X-axis indicates run-time time in seconds.
55. being registered according to the description length of random subsets of size 4. A choice of subset changes every 10 iterations. It can be seen that the score goes lower, but the time required is then greater.
56. A multi-resolution approach illustrated. Coarser representations are shown at the top levels and the original image lies at the bottom.
57. Bag of pixels illustrated versus one conventional approach.
58. Reparameterisation along the curve.
59. actual set of bump data. Different instances are indicated by distinct colours (or shades).
60. Brain image warping. Points on the skull depict knot-points for the splines.
61. The dependencies structure of AART.