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This paper describes a 3D SLAM system using information from an actuated laser scanner and camera installed on a mobile robot. The laser samples the local geometry of the environment and is used to incrementally build a 3D point-cloud map of the workspace. Sequences of images from the camera are used to detect loop closure events (without reference to the internal estimates of vehicle location) using a novel appearance-based retrieval system. The loop closure detection is robust to repetitive visual structure and provides a probabilistic measure of confidence. The images suggesting loop closure are then further processed with their corresponding local laser scans to yield putative Euclidean image-image transformations. We show how naive application of this transformation to effect the loop closure can lead to catastrophic linearization errors and go on to describe a way in which gross, pre-loop closing errors can be successfully annulled. We demonstrate our system working in a challenging, outdoor setting containing substantial loops and beguiling, gently curving traversals. The results are overlaid on an aerial image to provide a ground truth comparison with the estimated map. The paper concludes with an extension into the multi-robot domain in which 3D maps resulting from distinct SLAM sessions (no common reference frame) are combined without recourse to mutual observation