Human skull is an important body structure for jaw movement and facial mimic simulations. Surface head can be reconstructed using 3D scanners in a straightforward way. However, internal skull is challenging to be generated when only external information is available. Very few studies in the literature focused on the skull generation from outside head information, especially in a subject-specific manner with a complete skull. Consequently, this present study proposes a novel process for predicting a subject-specific skull with full details from a given head surface using a statistical shape modeling approach. Partial least squared regression (PLSR)–based method was used. A CT image database of 209 subjects (genders—160 males and 49 females; ages—34–88 years) was used for learning head-to-skull relationship. Heads and skulls were reconstructed from CT images to extract head/skull feature points, head/skull feature distances, head–skull thickness, and head/skull volume descriptors for the learning process. A hyperparameter turning process was performed to determine the optimal numbers of head/skull feature points, PLSR components, deformation control points, and appropriate learning strategies for our learning problem. Two learning strategies (point-to-thickness with/without volume descriptor and distance-to-thickness with/without volume descriptor) were proposed. Moreover, a 10-fold cross-validation procedure was conducted to evaluate the accuracy of the proposed learning strategies. Finally, the best and worst reconstructed skulls were analyzed based on the best learning strategy with its optimal parameters. The optimal number of head/skull feature points and deformation control points are 2300 and 1300 points, respectively. The optimal number of PLSR components ranges from 4 to 8 for all learning configurations. Cross-validation showed that grand means and standard deviations of the point-to-thickness, point-to-thickness with volumes, distance-to-thickness, and distance-to-thickness with volumes learning configurations are 2.48 ± 0.27 mm, 2.46 ± 0.19 mm, 2.46 ± 0.15 mm, and 2.48 ± 0.22 mm, respectively. Thus, the distance-to-thickness is the best learning configuration for our head-to-skull prediction problem. Moreover, the mean Hausdorff distances are 2.09 ± 0.15 mm and 2.64 ± 0.26 mm for the best and worst predicted skull, respectively. A novel head-to-skull prediction process based on the PLSR method was developed and evaluated. This process allows, for the first time, predicting 3D subject-specific human skulls from head surface information with a very good accuracy level. As perspective, the proposed head-to-skull prediction process will be integrated into our real-time computer-aided vision system for facial animation and rehabilitation.

Graphical abstract

人体头骨是下巴运动和面部模仿模拟的重要身体结构。可以使用3D扫描仪以直接的方式重建表面头。但是，只有外部信息可用时，内部颅骨很难生成。文献中很少有研究集中于从外部头部信息生成颅骨，特别是针对特定受试者的完整颅骨。因此，本研究提出了一种使用统计形状建模方法从给定头部表面预测具有完整细节的特定对象头骨的新颖方法。使用了基于偏最小二乘回归（PLSR）的方法。使用209名受试者（性别-160名男性和49名女性；年龄-34-88岁）的CT图像数据库来学习头颅关系。从CT图像中重建头部和颅骨，以提取头部/颅骨特征点，头部/颅骨特征距离，头部-颅骨厚度以及头部/颅骨体积描述符，以进行学习。执行了一个超参数车削过程，以确定头部/头骨特征点，PLSR组件，变形控制点的最佳数量，以及针对我们的学习问题的适当学习策略。提出了两种学习策略（带/不带体积描述符的点到厚度和带/不带体积描述符的距离到厚度）。此外，进行了十次交叉验证，以评估所提出学习策略的准确性。最后，根据最佳学习策略及其最佳参数，分析了最佳和最差的重建头骨。头部/头骨特征点和变形控制点的最佳数量分别为2300和1300点。对于所有学习配置，PLSR组件的最佳数量范围是4到8。交叉验证显示，点对厚度，点对厚度随体积，距离对厚度以及距离对厚度随学习配置的较大平均值和标准偏差为2.48±0.27 mm，2.46±分别为0.19毫米，2.46±0.15毫米和2.48±0.22毫米。因此，厚度到距离是针对我们的头到头骨预测问题的最佳学习配置。此外，最佳和最差预测头骨的平均Hausdorff距离分别为2.09±0.15 mm和2.64±0.26 mm。开发并评估了一种基于PLSR方法的新颖的头颅预测过程。此过程首次允许从头部表面信息以非常好的准确性级别预测3D对象特定的人类头骨。从角度来看，建议的从头到脑的预测过程将被集成到我们的实时计算机辅助视觉系统中，以进行面部动画和康复。

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