Research regarding the similarity measurements of 3D craniofacial models (including 3D skull and face models) is an important research direction in fields such as archaeology, forensic science, and anthropology and represents a meaningful and challenging task. Its major challenges are the fact that 3D skulls are geometric models with multiple holes and complex topologies, there are facial expression changes on the 3D faces. Therefore, the general 3D shape similarity measurements, which are sensitive to boundaries and expression changes, make it impossible to simultaneously measure skull and face similarity. In this paper, we define a 3D signature to describe the pure intrinsic structure and distinguish the similar basic shape and complex topology of 3D skulls and faces: the harmonic wave kernel signature (HWKS). The HWKS is a point descriptor involving the Laplace–Beltrami operator, which is able to effectively extract geometrical and topological information from 3D skulls and faces. Based on the HWKS, we provide an effective pipeline for 3D skull and face similarity measurement by calculating the cosine distance between the HWKS values of 3D skulls and faces. By making comparisons with the wave kernel signature, the HWKS simultaneously describes both local and global properties of a shape. Results from a number of experiments have already shown that our framework is suitable for both measure 3D skull similarity and face similarity, and more importantly, measuring skull similarity and face similarity are two independent processes although using the same framework. By using the same measurement method for 3D skull similarity and face similarity, we observe an effective craniofacial relationship under unified metrics: The change rate of skull similarity is generally consistent with the corresponding face similarity, indicating the correlation between the shape of the 3D skull and its corresponding 3D face shape. And our experimental results show the rationality and effectiveness of this method, which refers to the previous researchers measure the similarity of the reconstructed face from the original skull to reflect the similarity of the original skull.

中文翻译：

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基于谐波核特征的 3D 头骨和面部相似度测量

3D颅面模型（包括3D头骨和面部模型）的相似性测量研究是考古学、法医学和人类学等领域的重要研究方向，是一项有意义且具有挑战性的任务。其主要挑战在于，3D 头骨是具有多个孔和复杂拓扑结构的几何模型，3D 面部存在面部表情变化。因此，对边界和表情变化敏感的一般 3D 形状相似性测量使得无法同时测量头骨和面部相似性。在本文中，我们定义了一个 3D 签名来描述纯内在结构并区分 3D 头骨和面部的相似基本形状和复杂拓扑：谐波核签名（HWKS）。HWKS 是一个涉及拉普拉斯-贝尔特拉米算子的点描述符，它能够有效地从 3D 头骨和面部提取几何和拓扑信息。基于 HWKS，我们通过计算 3D 头骨和人脸的 HWKS 值之间的余弦距离，为 3D 头骨和人脸相似性测量提供了有效的管道。通过与波核特征进行比较，HWKS 同时描述了形状的局部和全局特性。大量实验的结果已经表明，我们的框架适用于测量 3D 头骨相似度和人脸相似度，更重要的是，尽管使用相同的框架，测量头骨相似度和人脸相似度是两个独立的过程。通过对3D头骨相似度和人脸相似度使用相同的测量方法，我们在统一度量下观察到有效的颅面关系：头骨相似度的变化率与对应的人脸相似度大体一致，表明 3D 头骨的形状与其对应的 3D 人脸形状之间存在相关性。并且我们的实验结果证明了该方法的合理性和有效性，该方法是指之前的研究人员通过测量原始头骨重建人脸的相似度来反映原始头骨的相似度。