The goal of the talk is to present the results contained in Fryers, Kaminski, Teicher "Some application of algebraic curves to computational vision", The first part will be a primer in projective algebraic geometry, working up to understanding the role of Kruppa's equation for the absolute conic in the reconstruction problem in computer vision. The authors' generalization of Kruppa's equation to higher genus, non planar curves will then be presented, leading to their main results in 3D reconstruction.