Many image processing applications rely on partitioning an image into disjoint regions whose pixels are 'similar.' The watershed and waterfall transforms are established mathematical morphology pixel clustering techniques. They are both relevant to modern applications where groups of pixels are to be decided upon in one go, or where adjacency information is relevant. We introduce three new parallel partitioning algorithms for GPUs. By repeatedly applying watershed algorithms, we produce waterfall results which form a hierarchy of partition regions over an input image. Our watershed algorithms attain competitive execution times in both 2D and 3D, processing an 800 megavoxel image in less than 1.4 sec. We also show how to use this fully deterministic image partitioning as a pre-processing step to machine learning based semantic segmentation. This replaces the role of superpixel algorithms, and results in comparable accuracy and faster training times.