Craniofacial reconstruction is to predict the 3D facial geometry according to the internal relationship between the skull and face, which is widely applied in the field of criminal investigation, archaeology, forensic medicine and so on. In this paper, utilizing the inherent advantage of geodesic to encode craniofacial geometry, we propose a heat flow geodesic grid regression (HF-GGR) model to facilitate craniofacial reconstruction. Our algorithm consists of three steps. In the first step, we extract the nose-tip rooted geodesic distance field and discretize it into a radial grid representation. Then in the second step, we generate geodesic grid of target skull appearance by utilizing the partial least squares regression (PLSR) method. Finally in the third step, we reconstruct the face of target skull according to the geodesic grid and face statistical model. We have conducted experiments on a data set with 213 pairs of craniofacial data. The extensive experimental results show that our algorithm can achieve accurate reconstruction results with faster speed and fewer geodesic grid points than the state-of-the-art method.

颅面重建是根据颅骨与面部之间的内部关系来预测3D面部几何形状，已广泛应用于刑事调查，考古，法医学等领域。在本文中，利用测地线的固有优势对颅面几何进行编码，我们提出了一种热流测地线网格回归（HF-GGR）模型来促进颅面的重建。我们的算法包括三个步骤。第一步，我们提取鼻尖根部的测地距离场并将其离散化为径向网格表示。然后，在第二步中，我们利用偏最小二乘回归（PLSR）方法生成目标头骨外观的测地线网格。最后在第三步中 我们根据测地线网格和人脸统计模型重建目标头骨的人脸。我们对包含213对颅面数据的数据集进行了实验。广泛的实验结果表明，与最新方法相比，我们的算法可以更快的速度和更少的测地网格点实现准确的重建结果。