Many approaches to 3D image segmentation are based on hierarchical clustering of supervoxels into image regions. Here we describe a distributed algorithm capable of handling a tremendous number of supervoxels. The algorithm works recursively, the regions are divided into chunks that are processed independently in parallel by multiple workers. At each round of the recursive procedure, the chunk size in all dimensions are doubled until a single chunk encompasses the entire image. The final result is provably independent of the chunking scheme, and the same as if the entire image were processed without division into chunks. This is nontrivial because a pair of adjacent regions is scored by some statistical property (e.g. mean or median) of the affinities at the interface, and the interface may extend over arbitrarily many chunks. The trick is to delay merge decisions for regions that touch chunk boundaries, and only complete them in a later round after the regions are fully contained within a chunk. We demonstrate the algorithm by clustering an affinity graph with over 1.5 trillion edges between 135 billion supervoxels derived from a 3D electron microscopic brain image.
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