Abstract The past 20 years has seen a progressive evolution of computer vision algorithms for unsupervised 2D image segmentation. While earlier efforts relied on Markov random fields and efficient optimization (graph cuts, etc.), the next wave of methods beginning in the early part of this century were, in the main, stovepiped. Of these 2D segmentation efforts, one of the most popular and, indeed, one that comes close to being a state of the art method is the ultrametric contour map (UCM). The pipelined methodology consists of (i) computing local, oriented responses, (ii) graph creation, (iii) eigenvector computation (globalization), (iv) integration of local and global information, (v) contour extraction, and (vi) superpixel hierarchy construction. UCM performs well on a range of 2D tasks. Consequently, it is somewhat surprising that no 3D version of UCM exists at the present time. To address that lack, we present a novel 3D supervoxel segmentation method, dubbed 3D UCM, which closely follows its 2D counterpart while adding 3D relevant features. The methodology, driven by supervoxel extraction, combines local and global gradient-based features together to first produce a low-level supervoxel graph. Subsequently, an agglomerative approach is used to group supervoxel structures into a segmentation hierarchy with explicitly imposed containment of lower-level supervoxels in higher-level supervoxels. Comparisons are conducted against state of the art 3D segmentation algorithms. The considered applications are 3D spatial and 2D spatiotemporal segmentation scenarios. For the latter comparisons, we present results of 3D UCM with and without optical flow video pre-processing. As expected, when motion correction beyond a certain range is required, we demonstrate that 3D UCM in conjunction with optical flow is a very useful addition to the pantheon of video segmentation methods.