Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call "relative affine structure". Via a number of corollaries of our main results we show that our framework unifies previous work --- including Euclidean, projective and affine --- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

Automatically Recovering Geometry and Texture from Large Sets of Calibrated Images

Three-dimensional models which contain both geometry and texture have numerous applications such as urban planning, physical simulation, and virtual environments. A major focus of computer vision (and recently graphics) research is the automatic recovery of three-dimensional models from two-dimensional images. After many years of research this goal is yet to be achieved. Most practical modeling systems require substantial human input and unlike automatic systems are not scalable. This thesis presents a novel method for automatically recovering dense surface patches using large sets (1000's) of calibrated images taken from arbitrary positions within the scene. Physical instruments, such as Global Positioning System (GPS), inertial sensors, and inclinometers, are used to estimate the position and orientation of each image. Essentially, the problem is to find corresponding points in each of the images. Once a correspondence has been established, calculating its three-dimensional position is simply a matter of geometry. Long baseline images improve the accuracy. Short baseline images and the large number of images greatly simplifies the correspondence problem. The initial stage of the algorithm is completely local and scales linearly with the number of images. Subsequent stages are global in nature, exploit geometric constraints, and scale quadratically with the complexity of the underlying scene. We describe techniques for: 1) detecting and localizing surface patches; 2) refining camera calibration estimates and rejecting false positive surfels; and 3) grouping surface patches into surfaces and growing the surface along a two-dimensional manifold. We also discuss a method for producing high quality, textured three-dimensional models from these surfaces. Some of the most important characteristics of this approach are that it: 1) uses and refines noisy calibration estimates; 2) compensates for large variations in illumination; 3) tolerates significant soft occlusion (e.g. tree branches); and 4) associates, at a fundamental level, an estimated normal (i.e. no frontal-planar assumption) and texture with each surface patch.

Planning and Teaching Compliant Motion Strategies

This thesis presents a new high level robot programming system. The programming system can be used to construct strategies consisting of compliant motions, in which a moving robot slides along obstacles in its environment. The programming system is referred to as high level because the user is spared of many robot-level details, such as the specification of conditional tests, motion termination conditions, and compliance parameters. Instead, the user specifies task-level information, including a geometric model of the robot and its environment. The user may also have to specify some suggested motions. There are two main system components. The first component is an interactive teaching system which accepts motion commands from a user and attempts to build a compliant motion strategy using the specified motions as building blocks. The second component is an autonomous compliant motion planner, which is intended to spare the user from dealing with "simple" problems. The planner simplifies the representation of the environment by decomposing the configuration space of the robot into a finite state space, whose states are vertices, edges, faces, and combinations thereof. States are inked to each other by arcs, which represent reliable compliant motions. Using best first search, states are expanded until a strategy is found from the start state to a global state. This component represents one of the first implemented compliant motion planners. The programming system has been implemented on a Symbolics 3600 computer, and tested on several examples. One of the resulting compliant motion strategies was successfully executed on an IBM 7565 robot manipulator.