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We introduce Equivariant Neural Field Expectation Maximization (EFEM), asimple, effective, and robust geometric algorithm that can segment objects in3D scenes without annotations or training on scenes. We achieve suchunsupervised segmentation by exploiting single object shape priors. We make twonovel steps in that direction. First, we introduce equivariant shaperepresentations to this problem to eliminate the complexity induced by thevariation in object configuration. Second, we propose a novel EM algorithm thatcan iteratively refine segmentation masks using the equivariant shape prior. Wecollect a novel real dataset Chairs and Mugs that contains various objectconfigurations and novel scenes in order to verify the effectiveness androbustness of our method. Experimental results demonstrate that our methodachieves consistent and robust performance across different scenes where the(weakly) supervised methods may fail. Code and data available athttps://www.cis.upenn.edu/~leijh/projects/efem

EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision