颅面形态学一直以来都是法医学、人类学等领域的研究热点，随着三维扫描设备的普及，获取高精度的三维数据变得简单、方便。三维颅骨、颅面数据的大量出现，使得三维人脸曲面、颅骨曲面的相关研究成为计算机图形学与计算机视觉等学科所热衷的研究方向。三维颅骨的相似性度量与躺卧三维颅面数据如何矫正为直立数据在刑事侦查、颌面手术、模型检索、考古学、法医学和人类学等领域中都有着很重要的应用，因此快速、准确的进行颅骨相似度评价以及对躺卧姿态的三维颅面数据进行直立矫正是亟待研究的重要问题。本文以人类学、法医学的相关理论为研究基础，以计算机可视化为研究工具，借助微分几何相关知识，对颅骨的相似度评价以及躺卧姿态三维颅面模型的直立矫正进行了深入研究，主要工作包括：1. 数据预处理。通过CT机和三维扫描设备获取CT数据以及躺卧和直立两种姿态下的颅面数据并对它们进行重建、修复、去噪、光顺等处理，最后对模型进行配准、拼接以及分割等操作，使得所有的数据模型满足本文研究的需要。2. 提出基于径向曲线的Fréchet距离的三维颅骨相似性度量方法。该方法通过在经过填补处理的三维颅骨模型上提取从鼻根中心点发射的一组径向曲线，并基于两个三维颅骨模型上对应径向曲线的Fréchet距离度量它们的相似度。实验结果表明该方法不仅可以将不同人的颅骨区分开，而且可以给出反映不同人的颅骨模型之间相似度值的量化方法。3. 提出基于测地线的躺卧三维颅面模型的直立矫正研究方法。首先对每个颅面模型提取鼻尖点作为源点，并从此源点出发提取等角度间隔测地线，根据鼻尖点到测地线另一端点的测地距离等分每条测地线，把这些测地线上的等分点作为三维颅面模型的特征点。然后，计算样本空间中每个躺卧三维模型上的特征点到其直立模型上对应特征点的运动向量，并对这些特征点及其运动向量建立统计模型，统计两种不同姿态下模型的变化规律，最后通过此规律实现躺卧姿态颅面模型到直立姿态颅面模型的变形。

Craniofacial morphology study has always been a hot research in forensic medicine, anthropology fields and so on. With the popularity of three-dimensional scanning device, it is becoming more and more simple and convenient to achieve high-precision 3D model data. Research on 3D human face and skull has emerged as a critical issue in computer graphics, computer vision and etc. Similarity measure of 3D skull model and transfer 3D facial model in lying posture to upright are two critical issues, and have important application in criminal investigation, maxillofacial surgery, model retrieval, archaeology, forensic and other fields. The main research in the article includes:1. Data preprocess. Obtain CT data, lying down and upright craniofacial data by CT and three-dimensional scanner firstly, using the marching cubes algorithm to construct the polygonal mesh of 3D models, then using Geomagic Studio to preprocess models, such as repairing, denoising, smoothing and hole filling and so on. Finally, model registration, splicing and divide operation are take into consideration. All the data models must meet the needs of our study.2. 3D skull similarity measure based on Fréchet distance of Radial Curves. In our method, we first preprocess the Skull models, and then exact a set of radial curves from the center of nose root and the similarity between two Skull models is computed through Fréchet distance of all corresponding geodesics. Experimental results illustrate that our method not only distinguishes different person’s skull, but also reflects the quantified similarity of different persons’ skull models. It is a global method to measure 3D skull similarity.3. The method of correcting the 3D craniofacial model in lying posture based on Geodesic. Exacting geodesics with equal angle interval emanating from the nose tip point, and then divide those geodesics according to the geodesic distance from the nasal tip point to another endpoint of each geodesic. The next step is to calculate the motion vector that from the lying posture model’s feature points to vertical’s in model base. Establish statistical model for feature points and motion vector, we can obtain the model’s variation of the model in different attitudes. According to the feature points we can get a transformation finally.