This paper describes external camera-based shape estimation for continuum robots. Continuum robots have a continuous backbone made of sections which bend to produce changes of configuration. A major difficulty with continuum robots is the determination of the robot's shape, as there are no discrete joints. This paper presents a method for shape determination based on machine vision. Using an engineered environment and image processing from a high speed camera, shape determination of a continuum robot is achieved. Experimental results showing the effectiveness of the technique on our Elephant's Trunk Manipulator are presented.