Stereo vision based on algebraic curves

Stereo vision based on conics has received much attention by many authors. Conics have many features such as their matrix expression, efficient correspondence checking, abundance of conical shapes in the real world, etc. Extensions to higher algebraic curves met with limited success. We consider planar algebraic curves of an arbitrary degree n⩾2, and a fully calibrated stereo system. We propose closed form solutions to both correspondence and reconstruction problems. Although its complexity increases as the degree n goes up, the proposed algorithm is extremely efficient. Moreover it does not depend on the special feature of conics for n=2 as has been with many past works. We checked our algorithm using synthetic as well as real world images