this is a nice project. Luckily for you, this kind of anamorphosis doesn't require advanced maths. The only result you need is Thales theorem, and in fact you can probably do most of the work on sketches.
The basic idea is that if the real distance from the viewer to an object is multiplied by a factor k, then the size of the object should be multiplied by the same factor k.
In the example (Jim Bond), the elements look very much like scaled versions of the hand, leg, head, etc. You can in fact allow much more freedom than that: for instance, a deformed head could look like normal from the appropriate viewpoint.
On the other hand, there are also possible simplifications, i.e. cases when you can avoid deforming object by just scaling them. This is the case for almost-planar objects (like a door) under some condition (the real door has to be parallel to the "virtual" door), and this is the case for relatively small objects (like a door knob, or body parts in Bond's artwork), where slight deformation will keep unnoticed.
The best is to start with a sketch. Draw the view from above (to get the location on the ground), and the view from the side (to get the height). In each case, you should begin by choosing the viewer's location. Then draw the objects of the scene like they should be viewed, for instance a real-size door with a real-size door number on it (on the sketches from above and from the side, these are line segments, or rectangles). On this sketch, draw thin lines from the viewpoint through the corners of the door (cf. attached sketch). These lines determine where the corners of the real door (the one you will build) should be; anywhere they are on these lines, they will appear to be at the same point for the viewer. On the sketch, the real door is chosen to be parallel to the "virtual" door (the real-size one); this way, the real door is not deformed, it is just scaled by a factor that you can measure on the sketch. You can do the same for any object: draw what it should look like, then choose what you're going to build by picking points that keep being on the same line from the viewpoint.
This is the main idea; your imagination will do the rest!
If something is not clear, or not sufficiently precise, feel free to ask.