We'll discuss how to use GPUs to accelerate a common 3D spatial processing application, point cloud registration. Registration, or finding the relative rigid transform between two point clouds, forms a core component of many 3D vision algorithms such as object matching and environment reconstruction. We use the GPU to accelerate this process using a parallelized form of the Expectation Maximization (EM) algorithm. Using this novel EM construction can both accelerate registration as well as provide a natural geometric segmentation of the data, two processes that we show to be highly interrelated at the kernel level when deployed on a GPU. Finally, we discuss how GPU-accelerated registration can be used in the larger context of real-time 3D perception.