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This paper presents a novel approach to underwater terrain mapping for Autonomous Underwater Vehicles (AUVs) operating in close proximity to complex 3D environments. The proposed methodology creates a probabilistic elevation map of the terrain using a monocular image learning-based scene range estimator as a sensor. This scene range estimator can filter transient objects such as fish and lighting variations. The mapping approach considers uncertainty in both the estimated scene range and robot pose as the AUV moves through the environment. The resulting elevation map can be used for reactive path planning and obstacle avoidance to allow robotic systems to approach the underwater terrain as closely as possible. The performance of our approach is evaluated in a simulated underwater environment by comparing the reconstructed terrain to ground truth reference maps, as well as demonstrated using AUV field data collected within in a coral reef environment. The simulations and field results show that the proposed approach is feasible for obstacle detection and range estimation using a monocular camera in reef environments.