Anatomical Landmark-Guided Deformation Methods for Cranial Modeling
Authors: Liu Zhuoman , Luximon Yan , Lin Ng Wei , Chung Eric , Zhang Jie 
Published: June 2023

Automatic cranial model deformation has a significant impact on the ergonomic design of headgears. It benefits product design by providing accurate human cranial measurements while automatically deforming to target shapes. With the development of automatic deformation methods, cranial modeling can now be handled efficiently rather than manually customized. Furthermore, previous studies have shown that integrating anatomical landmarks in deformation methods can improve modeling accuracy. Hence, this study provides anatomical definitions of cranial landmarks, including 51 skull landmarks and 14 mandible landmarks.This study compares three different landmark-guided deformation methods using the above anatomic landmarks, including Landmark-Guided Coherent Point Drift (LGCPD), Neural Deformation Pyramid (NDP), and the registration part in SCULPTOR (S-ARAP). These three methods treat the automatic deformation problem as a task of probability density estimation, hierarchical deformation decomposition, and local rigidity preservation, respectively. However, LGCPD is computationally intensive, which means once the cranial model has many vertices, the computation consumes a large memory and runs slowly. Additionally, LGCPD is sensitive to obtain a suboptimal solution and results in a deformed model with a high shape variation. NDP simplifies the deformation problem by decomposing it into several sub-deformations. With Multi-Layer Perception (MLP), NDP can perform the deformation approximately 10 times faster than LGCPD. However, without the constraint of local rigidity, partial-to-partial deformation accumulates minor deformation errors from each sub-step, leading to unsatisfactory deformation results. S-ARAP uniformly samples control nodes and computes their influence weights on the source model's vertices using Radial Basis Function (RBF). The larger the distance between the node and the vertices, the higher the weight with a stronger influence. The as-rigid-as-possible (ARAP) term is then introduced to preserve the local rigidity of the deformed model with the calculated influence weights for the local regions. Therefore, S-ARAP can automatically deform the cranial model, particularly the skull part with complex geometries, to achieve a well-structured result. Moreover, the control node sampling speeds up the execution of deformation while using less memory than LGCPD. Instead of the decomposition in NDP, S-ARAP increases the number of control nodes in several stages to perform hierarchical deformation.Finally, with quantitative and qualitative experimental results, the study discusses and compares the suitability of these three deformation methods for automatic cranial modeling. The study computes Chamfer-Distance (CD) and Point-to-Plane Distance (PTPD) on the deformed results for quantitative comparisons. CD determines the distance between deformed vertices and the nearest vertices on the target model and vice versa. PTPD calculates the distance between the deformed vertices and the nearest plane on the target model to calculate the shape error. The maximum value in PTPD can help identify outliers in deformed results. Lower CD and PTPD values suggest a better match with the target. According to the experimental results, S-ARAP outperforms LGCPD and NDP in terms of CD and PTPD. Furthermore, the deformed data are visualized with a heatmap revealing the large deformation error, and S-ARAP shows the lowest fitting error on the deformed results. Thus, S-ARAP is a suitable method for automatic deformation on cranial modeling.