Continuum robots offer significant advantages for surgical intervention due to their down-scalability, dexterity, and structural flexibility. While structural compliance offers a passive way to guard against trauma, it necessitates robust methods for online estimation of the robot configuration in order to enable precise position and manipulation control. In this paper, we address the pose estimation problem by applying a novel mapping of the robot configuration to a feature descriptor space using stereo vision. We generate a mapping of known features through a supervised learning algorithm that relates the feature descriptor to known ground truth. Features are represented in a reduced sub-space, which we call eigen-features. The descriptor provides some robustness to occlusions, which are inherent to surgical environments, and the methodology that we describe can be applied to multi-segment continuum robots for closed-loop control. Experimental validation on a single-segment continuum robot demonstrates the robustness and efficacy of the algorithm for configuration estimation. Results show that the errors are in the range of 1°.