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

University Of Utah, Salt Lake City UT

Investigators

Abstract

Title --- CAREER: A Statistical Approach to Estimating 3D Manifolds From Range Data PI --- Ross T. Whitaker Institution --- University of Utah This 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.