Cool! I'm reminded of ray tracing specular spheres in a Cornell Box. ;) Specular surfaces has always been a gotcha in computer vision applications, especially in regards to tracking and recovering 3D surfaces. Initially reading the paper, one of the coolest things was using the Legendre transform to represent a curve (I had never heard of it before now). As the paper suggests this greatly simplifies the description of the geometry of the specular reflection in the 2D case.

Unfortunately, the 3D case is not as trivial. They end up introducing a new, "moving" coordinate system attached to reflected rays. Unfortunately, I have a hard time visualizing what this coordinate system looks like (anyone willing to help explain this?). The coordinate system aside though, they are able to recover an large amount of information such as image trajectories and caustic curves. Pretty neat!

I know that using computer renders is a "sin" in computer vision papers, but wouldn't the use of a ray tracer help various aspects of their research? Even though the ray tracer would produce a perfectly specular object (which doesn't exist in real life), I would think that they could still produce some meaningful results since they wouldn't have to deal with as many unknowns. This was just a though that I had.

These results are impressive considering how difficult this problem is. I would be interested to see what research has been done since 1996. Does anyone know if there have been papers addressing the issue of moving specular objects?