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

标题-Career：从Range DataPI估计3D流形的统计方法-Ross T.WhitakerInstitution-犹他大学这个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、法医、教学和医学在内的广泛应用中非常重要。测距设备通常扫描一束能量，从物体表面收集数百万个3D测量数据，但它们有一些限制。首先，由于并非所有对象都从单个视点可见，因此单个扫描是不完整的。其次，每个单独的距离测量不一定是准确的，因为测量过程本身就有噪声。该策略是将来自不同角度的许多测量结果系统地融合在一起，以创建准确、完整的3D模型。该项目研究了与这一过程相关的一些基本数学问题，然后研究如何在实际数据上实施和演示这一理论。测距设备通过反射不同类型材料之间的界面能量来测量到对象的距离，但它们提供了从一组曲面到一组2D深度图的噪声、数学上的复杂和高度非线性的转换。这个项目将开发从这种数据中估计流形的统计方法，从而推广估计理论的当前技术状态，估计理论主要涉及估计函数或场。因此，目标是为三维曲面重建提供一个通用的、完整的、实用的基础。策略是找到使后验概率最大化的曲面，条件是从不同的角度进行距离测量的集合。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征的先验知识。这项工作将解决与建立3D模型的统计方法有关的一些重要问题，包括更好的传感器模型、高阶先验、快速和健壮的算法以及更广泛的应用。这些发展将构成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三维表面重建问题。

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.