AINR: Automated intrinsic non-rigid registration for accuracy qualification of complex freeform products in 3D printing

Non-rigid shape registration identifies the optimal non-rigid transformation between an actual product and its intended design to characterize their geometric dissimilarities. This transformation is usually determined by iteratively minimizing point-wise distances to match points with point-wise rigid motion. However, freeform products may exhibit complex spatial patterns of shape deviation, leading to premature iteration termination due to tradeoffs among local regions. One solution is to segment the complex design into semantic features and perform segment-wise rigid registration. Segment boundaries are typically placed along high-curvature regions, where deviations are more likely occur in 3D printing. However, since boundaries are generally more prone to registration errors, these segment-based methods may result in inaccurate deviation characterization. To enhance qualification of shape accuracy, we propose AINR-an Automated Intrinsic Non-rigid Registration method that prioritizes high-curvature, deviation-prone regions during both segmentation and registration. We introduce a curvature-informed surface point clustering technique for automated segmentation. Within corresponding segments, high-curvature regions are matched based on similar intrinsic geometries rather than point-wise distances, enabling more flexible and accurate transformations. In particular, the Teichmüller map is adopted to determine the unique, optimal and intrinsic transformation between surface points. The methodology has been validated through simulations and case studies.