Image transformation library

I need you to direct me to a free image transformation library, preferably written in delphi or at least such one that can be used with delphi and with a good manual.
I need to do my student’s term work like in these photomontages

To start with, I need to know the image-transformation names so I can find info on them.

This one is interesting as the image was adjusted to fit a cylindral surface.

which probably required to cut of the hand earlier, then you add the second layer as the user’s picture and over it you put the third layer as the hand that was previously cut off, right?

and this may be of use to me too.