Streaming Connected Component Computation for Trillion Voxel Images

We describe a highly scalable algorithm for computing connected components in large binary 3D grids. We employ a streaming version of the union-find algorithm that—as it processes the voxel grid row-by-row and layer-by-layer—only maintains the component structure along a single layer of active rows. We can process voxel grids whose sizes are three orders of magnitude larger than what the best previously reported method is capable of and still use less than half the memory. For example, given a random binary grid of 10,000×10,000×10,000 (= one trillion) voxels our method can count the number of components and report the volume and surface area of each using no more than 350 MB of main memory.