This paper reminds me of the literature for intrinsic and extrinsic camera calibration and the journey to making camera calibration a known thing, as it is today. This paper makes known one way to estimate generic specular surface geometry using patterns, and I'm sure transparent surfaces as a known thing are forthcoming as well, if not already. I felt this was one of those "Oh, why didn't i think of that" kind of papers.

I like the idea introduced in the beginning saying that the same math can be applied towards a situation where a LCD projector projects a calibrated pattern onto the specular surface and reflecting it onto a reference plane. I otherwise think that this algorithm is kinda weak since it requires knowing x_i (the imaged of the reflected pattern point). What if the specular surface were really small?

The monge representation and some of the symbols used in the paper are a bit confusing for me on one sitting with this paper. I'm looking forward to hearing about this on tuesday for sure.