三维颅面相似度比较的研究
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摘要
计算机辅助颅面复原是随着计算机的发展而兴起的一门新技术,它以现代解剖学为理论依据,以传统颅面复原技术为基础,是通过计算机的辅助对活体颅面进行修复和重塑、对未知颅骨进行面貌复原的技术。这项技术可应用在考古学、人类学、医学、公共安全系统等多个领域,具有广阔的应用发展前景。迄今在颅面复原算法方面已开展了大量工作,但颅面复原后期结果评价研究却仍是一个挑战性的难题,三维颅面相似度比较正是其中重要一环。该项研究可为颅面复原结果定性和定量的分析提供基础,并可应用在颅面复原前筛选颅面、颅面检索等其他方面。本文以此为研究背景,针对三维颅面的特点提取其形状特征,对三维颅面几何相似度比较展开研究,给出三维颅面比较的方法。
论文主要工作及创新点如下：
1.提出一种结合局部平面对称和力矩平衡的三维模型姿态估计方法。通过三维模型的CPCA坐标平面确立其全局对称平面和初始姿态,提出局部对称长度比度量三维模型的局部对称性,使用最大局部对称长度比确立具有局部对称性的三维模型的最终姿态,使用力矩平衡原理确立不具有局部对称性的三维模型的最终姿态。
2.基于上述三维模型姿态估计的方法,提出估计三维颅面姿态的方法。考虑到三维颅面更需要在面部进行对齐,为此通过对齐颅面正中矢状面轮廓的办法估计颅面姿态。求出颅面的正中矢状面轮廓线,每间隔一个固定角度对轮廓线进行采样,得到能够反映其形状的轮廓点。将不同颅面的轮廓点进行对齐,从而得到颅面的最终姿态。最后对本文使用的数据库中的颅面进行了姿态估计。
3.提出使用Principal Warps进行颅面相似度比较的算法。将Principal Warps扩展到两个三维模型同构特征点间的形状变形分析,进而将两个颅面的几何相似度比较看作是一个参考颅面到另一个颅面的弯曲变形,弯曲变形程度越小说明两个颅面越相似。首先选择对应颅面特征点,然后以薄板样条函数建立二者间的映射,计算两个颅面对应特征点的弯曲变形矩阵,并用参考颅面的Principal Warps为基表示该矩阵,在此基础上定义了颅面相似度的计算公式,从而实现对三维颅面几何相似度比较。
4.提出基于地图投影进行颅面相似度比较的方法。算法利用航海图常用的墨卡托投影将不可展的三维颅面模型展开成平面,然后引入大地高来反映三维颅面模型展开后的弯曲程度,最终形成展开曲面并将其划分成小曲面。选择改进锥曲率作为展开曲面离散网格点曲率的估算方法,计算每个小曲面的四个标量：大地高均值、大地高方差、锥曲率均值、锥曲率方差,以此作为衡量小曲面的四个属性,定义小曲面间的距离,进一步定义展开曲面间的距离,通过比较其距离来衡量颅面间的相似度。
5.提出描述三维模型形状变化的描述符：自变化形状描述符。选择一系列等间距互相平行的平面切割三维模型,得到一组模型的切片。定义两个相邻切片间的差来反映切片间的形状变化,将所有切片的差值组成的向量定义为三维模型的自变化形状描述符。该描述符反映了三维模型的形状变化趋势,可用来作为三维模型整体形状比较的依据。最后给出算法进行三维颅面相似度比较。
6.提出半径-相对角直方图算法。针对相对角直方图算法计算结果不稳定以及计算时间长的问题,首先确立三维颅面对称平面的法向量为计算参考的第一主轴,然后定义一组同心球壳,将三维颅面的点划分在不同的球壳区间内,分区计算不同区间内点的相对角,在此基础上定义一个区间的相对角分布,进一步得到三维颅面在所有球壳上的半径-相对角直方图。引入卡方距离计算颅面间的距离,进行颅面相似度比较。
Computer aided craniofacial reconstruction, an emerging technology based on modern anatomy and traditional technologies, is used to reshape the face of a living person or to restore the face on the skull of a dead. This technology has wide development prospects in many fields such as archaeology, anthropology, iatrology and public safety system. So far some progresses have been made in the study of construction, but construction effects evaluation is still a challenging and difficult scheme. A vital part of evaluation is comparison of craniofacial shape similarities, which can set the stage for the qualitative and quantitative analysis for construction effects and can further be used in cranioface screening and retrieval. This thesis is concerned with comparison of3D craniofacial shape similarities. According to the characteristics of3D craniofaces, this thesis investigates on a series of methods to extract the shape features of3D craniofaces and then to compare them. The main work of this thesis is summarized as follows:
1. A combined partial symmetry and moment balance method for pose estimation is presented. First CPCA coordinate planes of a3D model are computed to establish the model's symmetry planes and its initial pose. Then a new measure, which is called partial symmetry length ratio (PSLR), is introduced to judge whether the model is partial symmetry or not. If the model is partial symmetry, the pose with maximal PSLR is the estimated pose; otherwise moment balance is used to estimate the model's final pose.
2. A method of pose estimation for3D craniofaces is introduced based on the above method. When estimating poses of3D craniofaces, their faces need to be aligned at first. The median plane is selected to solve this problem. For a cranioface the contour of its median plane is computed. Corresponding to a fixed angular sampling interval the contour is resampled to get a set of points, which can represent the shape of the median plane. The point set is aligned to another well-aligned set to get the final pose of the cranioface. The method was used to estimate the poses of all craniofaces in our database.
3. A method of comparison of3D craniofacial shape similarities based on principal warps is proposed. In our approach principal warps are extended to analyze shape deformation between the homologous landmarks of3D models. And comparison of two craniofaces is regarded as the deformation of the referenced one into the other. The more similar they are, the smaller deformation is. First the homologous landmarks are selected from the two craniofaces. Then thin-plate spline is used to establish a map between them and to compute a bending transformation matrix. The matrix can be represented by new bases, which are the principal warps of the referenced cranioface. And on that basis, the similarity formula is defined to compare craniofacial shape similarities.
4. A method of comparison of craniofacial similarities based on map projection is developed. Mercator projection, which is commonly used for navigation, is introduced to map3D cranioface on a flat surface. Then geodetic height is represented the curvature of the surface. Thus a developed curving surface is got and is divided into small cells. An improved cone-curvature estimation method is developed to compute the curvature of the vertices in the cells. Four measures, which is height mean, height variance, cone-curvature mean and cone-curvature variance, are used to define the distance between each cell, and further to define the distance between two curving surfaces. Craniofacial similarities are compared by the distance.
5. A shape descriptor, self-difference shape descriptor (SDSD), is proposed to describe the shape of3D model. A set of parallel planes with equal interval are selected to cut a model. Each plane intersects with the model and the set of the intersection points is called a slice. All slices will represent the shape of the model. The difference of two neighboring slices will reflect local shape variation of the model. Therefore SDSD is defined as a vector, whose component consists of the difference. SDSD can represent shape variation trend of the model. Supposing different models have different shape variation trends, this descriptor can be used to represent3D models. Lastly a computing method is given to compare similarities of craniofaces.
6. A method of radius relative angle-context distribution (RRACD) is introduced to solve the problems in traditional RACD methods, such as unstable results and long-time computation. The normal of the symmetry plane of a cranioface is regarded as the principal axis instead of the first PCA axis. Then a group of concentric spherical shells are constructed to partition the vertices of the cranioface into different shell sections. For each section the relative angle-context distribution is defined by relative angles of the vertices inside it. Thus RRACD is the distributions of all sections. Finally chi-square distance is used to measure craniofacial distance and to compare craniofaces.
论文主要工作及创新点如下：
1.提出一种结合局部平面对称和力矩平衡的三维模型姿态估计方法。通过三维模型的CPCA坐标平面确立其全局对称平面和初始姿态,提出局部对称长度比度量三维模型的局部对称性,使用最大局部对称长度比确立具有局部对称性的三维模型的最终姿态,使用力矩平衡原理确立不具有局部对称性的三维模型的最终姿态。
2.基于上述三维模型姿态估计的方法,提出估计三维颅面姿态的方法。考虑到三维颅面更需要在面部进行对齐,为此通过对齐颅面正中矢状面轮廓的办法估计颅面姿态。求出颅面的正中矢状面轮廓线,每间隔一个固定角度对轮廓线进行采样,得到能够反映其形状的轮廓点。将不同颅面的轮廓点进行对齐,从而得到颅面的最终姿态。最后对本文使用的数据库中的颅面进行了姿态估计。
3.提出使用Principal Warps进行颅面相似度比较的算法。将Principal Warps扩展到两个三维模型同构特征点间的形状变形分析,进而将两个颅面的几何相似度比较看作是一个参考颅面到另一个颅面的弯曲变形,弯曲变形程度越小说明两个颅面越相似。首先选择对应颅面特征点,然后以薄板样条函数建立二者间的映射,计算两个颅面对应特征点的弯曲变形矩阵,并用参考颅面的Principal Warps为基表示该矩阵,在此基础上定义了颅面相似度的计算公式,从而实现对三维颅面几何相似度比较。
4.提出基于地图投影进行颅面相似度比较的方法。算法利用航海图常用的墨卡托投影将不可展的三维颅面模型展开成平面,然后引入大地高来反映三维颅面模型展开后的弯曲程度,最终形成展开曲面并将其划分成小曲面。选择改进锥曲率作为展开曲面离散网格点曲率的估算方法,计算每个小曲面的四个标量：大地高均值、大地高方差、锥曲率均值、锥曲率方差,以此作为衡量小曲面的四个属性,定义小曲面间的距离,进一步定义展开曲面间的距离,通过比较其距离来衡量颅面间的相似度。
5.提出描述三维模型形状变化的描述符：自变化形状描述符。选择一系列等间距互相平行的平面切割三维模型,得到一组模型的切片。定义两个相邻切片间的差来反映切片间的形状变化,将所有切片的差值组成的向量定义为三维模型的自变化形状描述符。该描述符反映了三维模型的形状变化趋势,可用来作为三维模型整体形状比较的依据。最后给出算法进行三维颅面相似度比较。
6.提出半径-相对角直方图算法。针对相对角直方图算法计算结果不稳定以及计算时间长的问题,首先确立三维颅面对称平面的法向量为计算参考的第一主轴,然后定义一组同心球壳,将三维颅面的点划分在不同的球壳区间内,分区计算不同区间内点的相对角,在此基础上定义一个区间的相对角分布,进一步得到三维颅面在所有球壳上的半径-相对角直方图。引入卡方距离计算颅面间的距离,进行颅面相似度比较。
Computer aided craniofacial reconstruction, an emerging technology based on modern anatomy and traditional technologies, is used to reshape the face of a living person or to restore the face on the skull of a dead. This technology has wide development prospects in many fields such as archaeology, anthropology, iatrology and public safety system. So far some progresses have been made in the study of construction, but construction effects evaluation is still a challenging and difficult scheme. A vital part of evaluation is comparison of craniofacial shape similarities, which can set the stage for the qualitative and quantitative analysis for construction effects and can further be used in cranioface screening and retrieval. This thesis is concerned with comparison of3D craniofacial shape similarities. According to the characteristics of3D craniofaces, this thesis investigates on a series of methods to extract the shape features of3D craniofaces and then to compare them. The main work of this thesis is summarized as follows:
1. A combined partial symmetry and moment balance method for pose estimation is presented. First CPCA coordinate planes of a3D model are computed to establish the model's symmetry planes and its initial pose. Then a new measure, which is called partial symmetry length ratio (PSLR), is introduced to judge whether the model is partial symmetry or not. If the model is partial symmetry, the pose with maximal PSLR is the estimated pose; otherwise moment balance is used to estimate the model's final pose.
2. A method of pose estimation for3D craniofaces is introduced based on the above method. When estimating poses of3D craniofaces, their faces need to be aligned at first. The median plane is selected to solve this problem. For a cranioface the contour of its median plane is computed. Corresponding to a fixed angular sampling interval the contour is resampled to get a set of points, which can represent the shape of the median plane. The point set is aligned to another well-aligned set to get the final pose of the cranioface. The method was used to estimate the poses of all craniofaces in our database.
3. A method of comparison of3D craniofacial shape similarities based on principal warps is proposed. In our approach principal warps are extended to analyze shape deformation between the homologous landmarks of3D models. And comparison of two craniofaces is regarded as the deformation of the referenced one into the other. The more similar they are, the smaller deformation is. First the homologous landmarks are selected from the two craniofaces. Then thin-plate spline is used to establish a map between them and to compute a bending transformation matrix. The matrix can be represented by new bases, which are the principal warps of the referenced cranioface. And on that basis, the similarity formula is defined to compare craniofacial shape similarities.
4. A method of comparison of craniofacial similarities based on map projection is developed. Mercator projection, which is commonly used for navigation, is introduced to map3D cranioface on a flat surface. Then geodetic height is represented the curvature of the surface. Thus a developed curving surface is got and is divided into small cells. An improved cone-curvature estimation method is developed to compute the curvature of the vertices in the cells. Four measures, which is height mean, height variance, cone-curvature mean and cone-curvature variance, are used to define the distance between each cell, and further to define the distance between two curving surfaces. Craniofacial similarities are compared by the distance.
5. A shape descriptor, self-difference shape descriptor (SDSD), is proposed to describe the shape of3D model. A set of parallel planes with equal interval are selected to cut a model. Each plane intersects with the model and the set of the intersection points is called a slice. All slices will represent the shape of the model. The difference of two neighboring slices will reflect local shape variation of the model. Therefore SDSD is defined as a vector, whose component consists of the difference. SDSD can represent shape variation trend of the model. Supposing different models have different shape variation trends, this descriptor can be used to represent3D models. Lastly a computing method is given to compare similarities of craniofaces.
6. A method of radius relative angle-context distribution (RRACD) is introduced to solve the problems in traditional RACD methods, such as unstable results and long-time computation. The normal of the symmetry plane of a cranioface is regarded as the principal axis instead of the first PCA axis. Then a group of concentric spherical shells are constructed to partition the vertices of the cranioface into different shell sections. For each section the relative angle-context distribution is defined by relative angles of the vertices inside it. Thus RRACD is the distributions of all sections. Finally chi-square distance is used to measure craniofacial distance and to compare craniofaces.
引文
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