A Computation-Aware Shape Loss Function for Point Cloud Completion

Learning-based point cloud completion tasks have shown potential in various critical tasks, such as object detection, assignment, and registration. However, accurately and efficiently quantifying the shape error between the predicted point clouds generated by networks and the ground truth remains challenging. While EMD-based loss functions excel in shape detail and perceived density distribution, their approach can only yield results with significant discrepancies from the actual EMD within a tolerable training time. To address these challenges, we first propose the initial price based on the auction algorithm, reducing the number of iterations required for the algorithm while ensuring the correctness of the assignment results. We then introduce an algorithm to compute the initial price through a successive shortest path and the Euclidean information between its nodes. Finally, we adopt a series of optimization strategies to speed up the algorithm and offer an EMD approximation scheme for point cloud problems that balances time loss and computational accuracy based on point cloud data characteristics. Our experimental results confirm that our algorithm achieves the smallest gap with the real EMD within an acceptable time range and yields the best results in end-to-end training.