Joint Correspondence Computation and Statistical Analysis of Geometric Models of Human Faces and Bodies

该建议解决了处理三维几何人脸和身体模型的问题，这些模型可以使用从激光测距扫描仪到结构光扫描仪和基于图像的系统的各种技术来获取。处理几何数据时的两个关键问题是对应计算和几何模型群体的统计分析，对应计算识别两个或更多个几何模型之间的内在对应部分，统计分析计算几何模型的概率分布。这两个问题是相互依存的。一方面，模型群体的统计分析需要对应信息。另一方面，利用形状分析计算出的概率分布可以稳健有效地计算对应信息。在本项目中，我们的目标是利用这种相互依赖性来共同解决这两个问题。我们的目标是专注于多线性概率分布，它可以用来分析不同的几何变化引起的不同模式的变化。例如，该模型可以用于统计分析具有不同面部表情的不同对象的人脸形状或不同姿势的不同对象的人体形状。我们希望通过联合解决这两个问题，找到比现有方法质量更高的对应关系。首先，我们专注于基本问题，如分析不同的张量分解，可用于计算多线性模型和使用这种张量分解的框架，优化对应。其次，我们专注于将开发的方法应用于原始数据扫描。这一步的主要挑战是算法的发展，是强大的噪声和丢失的data.The知识，使用开发的方法可以用于各种应用，如三维人脸和人体模型的重建或几何物体的识别。这种类型的问题在除了计算机视觉和计算机图形之外的领域中遇到，例如在医学和生物学应用中。

This proposal addresses the problem of processing 3-dimensional geometric human face and body models, which can be acquired using a variety of techniques from laser-range scanners to structured light scanners and image-based systems. Two key problems when processing geometric data are the correspondence computation, which identifies intrinsically corresponding parts between two or more geometric models, and the statistical analysis of a population of geometric models, which computes a probability distribution of the geometric models. These two problems are interdependent. One the one hand, the statistical analysis of a population of models requires correspondence information. On the other hand, the probability distribution computed using shape analysis can be used to compute correspondence information robustly and efficiently.In this project, we aim to use this interdependence to solve the two problems jointly. Our goal is to focus on multilinear probability distributions, which can be used to analyze different modes of variation caused by different geometric variations. For instance, this model can be used to statistically analyze shapes of human faces of different subjects with different facial expressions or shapes of human bodies of different subjects in different poses. We expect to find correspondences of significantly higher quality than existing methods by solving the two problems jointly.We plan to address this problem in two steps. First, we focus on fundamental problems, such as the analysis of different tensor decompositions that can be used to compute a multilinear model and the use of such tensor decompositions in a framework that optimizes correspondences. Second, we focus on applying the developed methods to raw data scans. The main challenge of this step is the development of algorithms that are robust with respect to noise and missing data.The knowledge gained using the developed methods can be used in various applications, such as the reconstruction of 3D human face and body models or the recognition of geometric objects. Problems of this type are encountered in areas besides computer vision and computer graphics, for instance in medical and biological applications.