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In this paper, we investigate the following question:whenperformingnextbestviewselectionforvolumetric 3D reconstruction of an object by a mobile robot equipped with a dense (camera-based) depth sensor, what formulation of information gain is best? To address this question, we propose several new ways to quantify the volumetric information (VI) contained in the voxels of a probabilistic volumetric map, and compare them to the state of the art with extensive simulated experiments. Our proposed formulations incorporate factors such as visibility likelihood and the likelihood of seeing new parts of the object. The results of our experiments allow us to draw some clear conclusions about the VI formulations that are most effective in different mobile-robot reconstruction scenarios. To the best of our knowledge, this is the first comparative survey of VI formulation performance for active 3D object reconstruction. Additionally, our modular software framework is adaptable to other robotic platforms and general reconstructionproblems,andwereleaseitopensourceforautonomous reconstruction tasks.