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The investigation of continuum robots has become an area of considerable interest in the last several years. Unlike conventional robotic manipulators which bend in discrete locations, continuum robots bend over continuous sections. One of the main issues that is hampering research in this area is the determination of the robot's shape. In this paper we present a shape-determining scheme that is based on machine vision. The approach uses a high speed camera, an engineered environment, and image processing to determine the shape of our continuum robot called the Elephant's Trunk Manipulator. We present experimental results showing the effectiveness of the technique.