W. Randolph Franklin, Salles Viana Gomes de Magalhães, and Eric N Landis. Fast 3-D Euclidean connected components. In John Krumm, editor, 3rd ACM SIGSPATIAL International Workshop on Spatial Gems (SpatialGems 2021). ACM, 2 nov 2021. URL: https://www.spatialgems.net/.
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Abstract

We present an efficient algorithm, with implementations, for computing the connected components within a 3-D cube of voxels, also known as the Euclidean union-find problem. There may be over $10^9$ voxels. The components may be 8-connected or 26-connected. Computing connected components has applications ranging from material failure in concrete under increasing stress to electrical conductivity in complex metal objects to elasticity in 3D printed parts. On key to efficiency is representing voxels by 1-D \emphruns of adjacent voxels. As a special case, 2-D connected components of images may easily be computed.

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