Generation of Data

It has been implicitly mentioned that presently only 1-D data is practically under consideration. In order to keep results consistent, much of the time was spent investigating a particular class of data - that which shall be referred to as the bump^7.6. The bump (a half-circle or ellipse) which was being generated varied in 3 separate ways:

**Figure:** Illustration of the three variation modes.
$\includegraphics[%% scale=0.7]{./Graphics/bump.eps}$

Dealing with each of the above variation types in turn, position refers to the horizontal placement of the bump, height refers to the peak value (judged by its Y-component) and width refers to a relative width for the bump (see Figure $[*]$ ). Later figures clarify what is meant by these properties visually. This synthetic data type was chosen due to few interesting and important attributes it possesses. It proves to be a difficult problem when treated as raw input for registration, but more importantly, it is in fact possible to know what one means by a correct answer to the problem. That correct solution is also feasible to identify^7.7. As the notion of models is used here persistently, one could expect the modes of variation found to reflect on the three pre-defined modes being position, height and width.

**Figure:** 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.
$\includegraphics[%% scale=0.7]{./Graphics/image_vectors.eps}$

Figure $[*]$ shows the data in another more fascinating way which can dynamically illustrate the change due to registration. This representation has been used to form registration videos and it will be definitely returned to in future experimentation.

**Figure:** Original data set of size 5 before any application of warps.
$\includegraphics[%% scale=0.3]{./Graphics/test_on_target_7-4.eps}$

Later in this section, it will be shown what effect warps have on this data. Moreover, it is important to mention that the algorithm was applied to different synthetic data types although this was rare. Comparison is better performed over the same standardised dataset. Other data was usually used for reasoning about the correctness of algorithms and error detection via more trackable debugging tasks.

**Figure:** A larger example of pixel representation for 1-D bump data. This is somewhat of an enhancement to Figure cap:Data-being-registered..
$\includegraphics[%% scale=0.6]{./Graphics/pixels.eps}$