Obtain an open source camera tracker (good options are Voodoo, from http://www.digilab.uni-hannover.de/docs/manual.html#download; and I believe there is one in recent Blender releases, Introduction to Camera Tracking).
Use it to obtain camera parameters from a video sequence.
Now model a simple object with Blender (or some other modeller), and render it with LuxRender (or some other renderer) using these camera parameters. The object should sit on a base, and you should have a light source (which need not be visible) causing the object to cast a shadow.
Composite the rendered sequence with the video, using the method of: Debevec, "Rendering Synthetic Objects into Real Scenes: Bridging Traditional and Image-based Graphics with Global Illumination and High Dynamic Range Photography", 1998, described in the notes or on Paul Debevec's web page here.
This is a straightforward exercise, because the manuals will largely show you how to do this. However, this covers several REALLY useful tricks, so it's worth knowing. This exercise is worth a total of 10 points; I will offer 8 points for doing a reasonable job, 9 points if there is no slide or wobble of the object, and 1 point for really cleverly chosen models or renderings.
You may do this exercise individually, in pairs, or in groups of three. Videos are due 10 April. Email them to me at email@example.com, with "CS419" in the header