The nature of continuum soft robots calls for novel perception solutions, which can provide information on the robot's shape while not substantially modifying their bodies' softness. One way to achieve this goal is to develop innovative and completely deformable sensors. However, these solutions tend to be less reliable than classic sensors for rigid robots. As an alternative, we consider here the use of monocular cameras. By admitting a small rigid component in our design, we can leverage well-established solutions from mobile robotics. We propose a shape sensing strategy that combines a SLAM algorithm with nonlinear optimization based on the robot's kinematic model. We prove the method's effectiveness in simulation and with experiments of a single-segment continuous soft robot with a camera mounted to the tip. We achieve mean relative translational errors below 9% simulations and experiments alike, and as low as 0.5% on average for some simulation conditions.@en