Fast and accurate shape-based registration

In many areas of science, engineering, medicine, and especially in the field of robotics, there is a need to establish a spatial mapping between two or more 3-dimensional (3-D) shape representations of an object. The registration problem is concerned with finding a spatial transformation which best aligns two object representations. Once this mapping is established, a variety of tasks can be performed using the aligned object representations including model-based localization, 3-D object recognition, real-time pose tracking and multi-modality sensor fusion. The research goals of this dissertation are the design, implementation and validation of fast and accurate methods for performing 3-D shape-based registration. Fast registration is achieved via speed enhancements to an existing registration method (the iterative closest point algorithm). The implemented enhancements increase registration speeds by a factor of nearly two orders of magnitude, and the resulting speeds are much higher than those previously reported in the literature. The ability to perform high-speed registration enables completely new registration applications. For example, this dissertation describes a system for tracking the position and orientation of arbitrarily-shaped objects at speeds of roughly 10 Hz using a high-speed range finder. The majority of this dissertation focuses on the problem of achieving and ensuring high accuracy shape-based registration. This goal is addressed via two processes: intelligent data selection and online accuracy estimation. Intelligent data selection is based on the observation that all data are not equally beneficial for performing accurate registration. Judicious selection and careful collection of a limited amount of data can result in better registration accuracy than random use of larger amounts of data. In this dissertation, two techniques are proposed for performing intelligent data selection: an optimization process (Constraint Synthesis), and a numerical analysis method which provides a criterion measure for the optimization process (Constraint Analysis). Registration experiments demonstrate that data configurations which are automatically synthesized using these methods can significantly increase registration accuracy. A fundamental problem in registration is knowing whether an estimated transformation satisfies accuracy requirements at the time of registration. A conventional root-mean-squared error, coupled with the criterion measure from constraint analysis provides the ability to estimate true registration accuracy online. This estimate can be used to guide the online collection of registration data by determining when additional data are required to satisfy accuracy requirements. While there are many areas to which registration can be applied, the chosen domain for this dissertation is medicine, and most of the results are presented in the context of computer-assisted surgery. Despite the specific nature of the chosen application area, the underlying ideas and methods have application to a broad range of registration problems.