To motivate model matching or fitting, one can argue that the previously constructed model involved a learning process which must somehow be exploited. For it is now known what objects of some type look like, it is possible to recognise and capture new objects of the same type.
It is still not trivial in any case how one should deform the model
to achieve an appearance instance that is valid. It is now a completely
opposite problem that users of this model can be faced with: how can
one model generate new instances after similar existing instances
generated that one model? In some sense, an inverted operation is
needed so that the model can be used in the opposite way to the means
by which it was created. Things are not very simple in reality and
the alteration of model values needs to be guided by some minimisation
(some of the next chapters elaborate on this with practical examples,
e.g. Chapter ) that obtains the matching which
is being sought. Unfortunately, in an expectedly high-dimensional
space as above, the process is almost endless unless extra knowledge
about this minimisation problem is provided and in advance and utilised.