  Interest in soft continuum arms has increased as their inherent material
elasticity enables safe and adaptive interactions with the environment. However
to achieve full autonomy in these arms, accurate three-dimensional shape
sensing is needed. Vision-based solutions have been found to be effective in
estimating the shape of soft continuum arms. In this paper, a vision-based
shape estimator that utilizes a geometric strain based representation for the
soft continuum arm's shape, is proposed. This representation reduces the
dimension of the curved shape to a finite set of strain basis functions,
thereby allowing for efficient optimization for the shape that best fits the
observed image. Experimental results demonstrate the effectiveness of the
proposed approach in estimating the end effector with accuracy less than the
soft arm's radius. Multiple basis functions are also analyzed and compared for
the specific soft continuum arm in use.

Robotics