CAREER: A Statistical Framework For Reconstructing 3D Manifolds From Range Data

标题-职业生涯：从范围数据估计三维流形的统计方法。Whitaker Institution- University of Utah该项目解决了如何使用测距设备（如激光测距扫描仪，声纳，超声波或雷达）的数据自动生成物体和场景的3D计算机模型的问题。 这样的3D计算机模型在包括国防监视、取证、教学和医学在内的广泛应用中是重要的。 距离测量设备通常扫描能量束以从物体表面收集数百万个3D测量值，但它们具有一些局限性。 首先，因为并非所有对象从单个视点可见，所以单个扫描是不完整。 其次，每个单独的距离测量不一定准确，因为测量过程固有地有噪声。 该策略是将来自不同角度的许多测量数据系统地融合在一起，以创建准确，完整的3D模型。 这个项目研究了与这个过程有关的一些基本数学问题，然后研究如何在真实的数据上实现和演示这个理论。测距设备通过反射不同类型材料之间界面的能量来测量物体的距离，但是它们提供了一个嘈杂的，数学上复杂的，高度非线性的从表面集合到一组2D深度图的转换。 本项目将开发用于从此类数据估计流形的统计方法，从而概括主要关注估计函数或场的估计理论的当前技术水平。 因此，我们的目标是提供一个通用的，完整的，和实际的基础，三维表面重建。 该策略是找到表面，最大限度地提高后验概率的条件下，从不同的观点采取的范围测量的集合。 重建框架是贝叶斯的;它包括传感器模型以及关于被建模的对象或场景的特性的先验知识。 这项工作将解决一些重要的问题，有关这种统计方法建立三维模型，包括更好的传感器模型，高阶先验，快速和强大的算法，以及更广泛的应用。 这些发展将包括一个基本的科学成果：将估计理论的基本原理推广到具有挑战性和及时性的3D表面重建问题。

Title --- CAREER: A Statistical Approach to Estimating 3D Manifolds From Range DataPI --- Ross T. WhitakerInstitution --- University of UtahThis project addresses the question of how to automatically generate 3D computer models of objects and scenes using data from a range finding device, such as a laser range scanner, sonar, ultrasound, or radar. Such 3D computer models are important in a wide range of applications including defense surveillance, forensics, teaching, and medicine. Range measuring devices typically sweep a beam of energy to gather many millions of 3D measurements from surfaces of objects but they have some limitations. First, because not all object are visible from a single point of view, a single sweep is incomplete. Second, each individual range measurement is not necessarily accurate because the measurement process is inherently noisy. The strategy is to systematically fuse together many measurements from different points of view in order to create accurate, complete 3D models. This project examines some of the fundamental mathematical questions pertaining to this process and then studies how to implement and demonstrate this theory on real data.Range-finding devices measure distances to objects by reflecting energy off of the interfaces between different types of materials, but they provide a noisy, mathematically complex, and highly nonlinear transformation from a collection of surfaces to a set 2D depth maps. This project will develop statistical methods for estimating manifolds from this kind of data, thereby generalizing the current state of the art in estimation theory, which is primarily concerned with estimating functions or fields. Thus, the goal is to provide a general, complete, and practical foundation for 3D surface reconstruction. The strategy is to find the surface that maximizes the posterior probability conditional on a collection of range measurements taken from different points of view. The reconstruction framework is Bayesian; it includes a sensor model as well as prior knowledge about the characteristics of the object or scenes being modeled. This work will address a number of important issues pertaining to this statistical methodology for building 3D models, including better sensor models, high-order priors, fast and robust algorithms, and broader applications. These developments will comprise a fundamental scientific result: the generalization of the basic principles of estimation theory to the challenging and timely problem of 3D surface reconstruction.