We propose a Parallel Banding Algorithm (PBA) on the GPU to compute the exact Euclidean Distance Transform (EDT) for a bi- nary image in 2D and higher dimensions. Partitioning the image into small bands to process and then merging them concurrently, PBA computes the exact EDT with optimal linear total work, high level of parallelism and a good memory access pattern. Thiswork is the first attempt to exploit the enormous power of the GPU in com- puting the exact EDT, while priorworks are only on approximation. Compared to these other algorithms in our experiments, our exact algorithm is still a few times faster in 2D and 3D for most input sizes. We illustrate the use of our algorithm in applications such as computing the Euclidean skeleton using the integer medial axis transform, performing morphological operations of 3D volumetric data, and constructing 2D weighted centroidal Voronoi diagrams.
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