In this talk, I will discuss two research projects that have little to do with each other, save the word "surface". In the first part of the talk, I will discuss how to find globally optimal, discrete minimal surfaces in polynomial time, and how this algorithm can be applied to the computer vision problem of shape from stereo. In the second part of the talk, I will discuss a system that takes an irregularly connected geometric mesh (of arbitrary genus), and approximates it with a geometry image: a completely regular n-by-n array of [x,y,z] values. This transformation, which requires topological unfolding and optimized surface parameterization, can be useful to unify image and geometric representations.