Abstract Unsupervised over-segmentation of an image into regions of perceptually similar pixels, known as superpixels, is a widely used preprocessing step in segmentation algorithms. Superpixel methods reduce the number of regions that must be considered later by more computationally expensive algorithms, with a minimal loss of information. Nevertheless, as some information is inevitably lost, it is vital that superpixels not cross object boundaries, as such errors will propagate through later steps. Existing methods make use of projected color or depth information, but do not consider three dimensional geometric relationships between observed data points which can be used to prevent superpixels from crossing regions of empty space. We propose a novel over-segmentation algorithm which uses voxel relationships to produce over-segmentations which are fully consistent with the spatial geometry of the scene in three dimensional, rather than projective, space. Enforcing the constraint that segmented regions must have spatial connectivity prevents label flflow across semantic object boundaries which might otherwise be violated. Additionally, as the algorithm works directly in 3D space, observations from several calibrated RGB+D cameras can be segmented jointly. Experiments on a large data set of human annotated RGB+D images demonstrate a signifificant reduction in occurrence of clusters crossing object boundaries, while maintaining speeds comparable to state-of-the-art 2D methods.