Soft continuum robots are highly flexible and adaptable, making them ideal for unstructured environments such as the human body and agriculture. However, their high compliance and maneuverability make them difficult to model, sense, and control. Current control strategies focus on Cartesian space control of the end-effector, but few works have explored full-body control. This study presents a novel image-based deep learning approach for closed-loop kinematic shape control of soft continuum robots. The method combines a local inverse kinematics formulation in the image space with deep convolutional neural networks for accurate shape control that is robust to feedback noise and mechanical changes in the continuum arm. The shape controller is fast and straightforward to implement; it takes only a few hours to generate training data, train the network, and deploy, requiring only a web camera for feedback. This method offers an intuitive and user-friendly way to control the robot's 3-D shape and configuration through teleoperation using only 2-D hand-drawn images of the desired target state without the need for further user instruction or consideration of the robot's kinematics.