In this work, we address the problem of robust segmentation of a continuum robot from images without the need for training data or markers. We present a method that leverages information about the kinematics of these robots to produce an estimate of the robot shape, which is refined through optimization over global image statistics. Our approach can be straightforwardly applied to any continuum robot design and is able to handle partial occlusions of the robot body, as well as challenging background conditions. We validate our method experimentally for a concentric tube robot in a simulated surgical environment and show that our method significantly outperforms a naive projection of the robot shape and color thresholding, which is commonly used in current vision-based estimation algorithms for these robots. Overall, this work has the potential to improve the viability of vision-based state estimation for continuum robots in real-world settings.