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

这一提议解决了处理三维几何人脸和身体模型的问题，可以使用从激光距离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得这些模型。处理几何数据时的两个关键问题是对应计算和统计分析，前者识别两个或多个几何模型之间本质上对应的部分，后者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，对总体模型的统计分析需要对应的信息。另一方面，形状分析计算出的概率分布可以用于稳健高效地计算对应信息，在本项目中，我们的目标是利用这种相互依赖来联合解决这两个问题。我们的目标是关注多线性概率分布，它可以用来分析由不同的几何变化引起的不同的变化模式。例如，该模型可以用来统计分析不同对象在不同姿势下不同面部表情或不同人体形状的人脸形状。我们希望通过联合解决这两个问题，找到比现有方法更高质量的对应。我们计划分两步解决这个问题。首先，我们专注于基本问题，例如可以用来计算多线性模型的不同张量分解的分析，以及在优化对应的框架中使用这种张量分解。其次，我们重点研究了已开发的方法在原始数据扫描中的应用。这一步骤的主要挑战是开发对噪声和丢失数据具有健壮性的算法。使用所开发的方法获得的知识可以用于各种应用，如三维人脸和身体模型的重建或几何对象的识别。这种类型的问题在计算机视觉和计算机图形学之外的领域中遇到，例如在医疗和生物应用中。

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.