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Warps

This short subsection adheres to a more local perspective - a perspective along the lines of which future research should move. The short part on diffeomorphism (Subsubsection ) introduced functions that map a group of pixels to new positions. These functions will now be permanently referred to as warps plainly because this is the terminology that is invariantly used in the literature. Due to practical considerations, the warps used are chosen to be rather elementary and therefore computationally inexpensive. Some will argue that more sophisticated warps will produce better results in a smaller period of time because a smaller number of these is required to reach overlap as explained previously. However, they may also damage some structures in regions that are better left untouched, as well as interfere with previous warps that supposedly did the right thing.

The warps currently used are round (also extensible to spherical) and they can be described by their location, radius and possibly depth. As expected, these warps are parameterised by their horizontal and vertical location, magnitude and radius. Many such warps are applied at different scales to the image. Their position is quite random and good results are committed and carried on to later iterations while bad ones get discarded. Towards the later stages of the algorithm, only small local warps, much as in the case of reparameterisation, will entail constructive results.

Figure: Warp applied to image. On the left: image before warp is applied; On the right: image after warping.

The choice of warps is quite arbitrary and their most preferable complexity level is still an issue of active discussion^3.15. The randomisation of the location at which warps are centred means that computation is saved on understanding the image and using any priorly-gained understanding. On the other hand, many warps are discarded in this way and wasted effort makes this method far less elegant.