The paper introduces a novel approach to the multi-model 3D registration problem, which aims to simultaneously recover the motion of multiple objects in cluttered point clouds. The authors propose an Expectation-Maximization (EM) algorithm to address this problem, which can handle outliers and does not require prior knowledge of the number of objects. The EM algorithm is based on a clustering interpretation of the problem, where each point is either associated with an object or considered an outlier. The paper provides theoretical conditions under which the EM algorithm converges to the ground truth, and evaluates the method on both synthetic and real-world datasets, demonstrating its effectiveness in recovering object motions and establishing dense correspondences with state-of-the-art scene flow methods. The experiments show that the proposed method outperforms existing baselines in terms of per-point error, rotation and translation error, and Intersection over Union (IoU).The paper introduces a novel approach to the multi-model 3D registration problem, which aims to simultaneously recover the motion of multiple objects in cluttered point clouds. The authors propose an Expectation-Maximization (EM) algorithm to address this problem, which can handle outliers and does not require prior knowledge of the number of objects. The EM algorithm is based on a clustering interpretation of the problem, where each point is either associated with an object or considered an outlier. The paper provides theoretical conditions under which the EM algorithm converges to the ground truth, and evaluates the method on both synthetic and real-world datasets, demonstrating its effectiveness in recovering object motions and establishing dense correspondences with state-of-the-art scene flow methods. The experiments show that the proposed method outperforms existing baselines in terms of per-point error, rotation and translation error, and Intersection over Union (IoU).