Abstract: Non-rigid point cloud registration has been a highly challenging problem due to the complexity and uncertainty of non-rigid object motion. Existing algorithms for non-rigid point cloud registration have suffered from a significant number of outliers in the registration results and limited robustness against noise input. To address these issues, researchers proposed a novel approach called the multi-head gated multi-layer perceptron motion decomposition algorithm.In this algorithm, the points in the 3D point cloud were first encoded using sine functions and then inputted into a multi-level multi-head gated multi-layer perceptron. By decomposing the motion, multi-head gated units were utilized at each level to handle outliers and noise, ultimately obtaining the motion increments for corresponding points in the final level. Throughout this process, the frequency of the sine function gradually increased with each level to capture the fluctuation patterns of non-rigid motion.To evaluate the effectiveness of the proposed algorithm, experiments were conducted on two datasets and compared against nine mainstream non-rigid point cloud registration methods using four evaluation metrics. The results demonstrated that the proposed algorithm achieved a reduction in endpoint error and outlier rate ranging from 1.84% to 18.8% and 5.61% to 30.76%, respectively. Moreover, it exhibited an improvement in the strict correctness registration rate and correct registration rate by 2.78% to 13.26% and 5.43% to 22.63%, respectively.Additionally, the registration time was reduced by a factor of 2 to 50. These experimental findings highlight the algorithm's ability to rapidly produce non-rigid point cloud registration results with a uniform and smooth point cloud distribution, free from outliers.