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.

The Perception of Subjective Surfaces

It is proposed that subjective contours are an artifact of the perception of natural three-dimensional surfaces. A recent theory of surface interpolation implies that "subjective surfaces" are constructed in the visual system by interpolation between three-dimensional values arising from interpretation of a variety of surface cues. We show that subjective surfaces can take any form, including singly and doubly curved surfaces, as well as the commonly discussed fronto-parallel planes. In addition, it is necessary in the context of computational vision to make explicit the discontinuities, both in depth and in surface orientation, in the surfaces constructed by interpolation. It is proposed that subjective surfaces and subjective contours are demonstrated. The role played by figure completion and enhanced brightness contrast in the determination of subjective surfaces is discussed. All considerations of surface perception apply equally to subjective surfaces.

FastAero – A Precorrected FFT – Fast Multipole Tree Steady and Unsteady Potential Flow Solver

In this paper a precorrected FFT-Fast Multipole Tree (pFFT-FMT) method for solving the potential flow around arbitrary three dimensional bodies is presented. The method takes advantage of the efficiency of the pFFT and FMT algorithms to facilitate more demanding computations such as automatic wake generation and hands-off steady and unsteady aerodynamic simulations. The velocity potential on the body surfaces and in the domain is determined using a pFFT Boundary Element Method (BEM) approach based on the Green’s Theorem Boundary Integral Equation. The vorticity trailing all lifting surfaces in the domain is represented using a Fast Multipole Tree, time advected, vortex participle method. Some simple steady state flow solutions are performed to demonstrate the basic capabilities of the solver. Although this paper focuses primarily on steady state solutions, it should be noted that this approach is designed to be a robust and efficient unsteady potential flow simulation tool, useful for rapid computational prototyping.

Shape from Contour

The problem of using image contours to infer the shapes and orientations of surfaces is treated as a problem of statistical estimation. The basis for solving this problem lies in an understanding of the geometry of contour formation, coupled with simple statistical models of the contour generating process. This approach is first applied to the special case of surfaces known to be planar. The distortion of contour shape imposed by projection is treated as a signal to be estimated, and variations of non-projective origin are treated as noise. The resulting method is then extended to the estimation of curved surfaces, and applied successfully to natural images. Next, the geometric treatment is further extended by relating countour curvature to surface curvature, using cast shadows as a model for contour generation. This geometric relation, combined with a statistical model, provides a measure of goodness-of-fit between a surface and an image contour. The goodness-of-fit measure is applied to the problem of establishing registration between an image and a surface model. Finally, the statistical estimation strategy is experimentally compared to human perception of orientation: human observers' judgements of tilt correspond closely to the estimates produced by the planar strategy.

Motion Planning with Six Degrees of Freedom

The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given high-level specifications of tasks and geometric models of the robot and obstacles. The Mover's problem is to find a continuous, collision-free path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the three-dimensional Mover's problem: given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collision-free path taking P from some initial configuration to a desired goal configuration. This thesis describes the first known implementation of a complete algorithm (at a given resolution) for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a six-dimensional configuration space (called C-Space). The C-Space obstacles, which characterize the physically unachievable configurations, are directly represented by six-dimensional manifolds whose boundaries are five dimensional C-surfaces. By characterizing these surfaces and their intersections, collision-free paths may be found by the closure of three operators which (i) slide along 5-dimensional intersections of level C-Space obstacles; (ii) slide along 1- to 4-dimensional intersections of level C-surfaces; and (iii) jump between 6 dimensional obstacles. Implementing the point navigation operators requires solving fundamental representational and algorithmic questions: we will derive new structural properties of the C-Space constraints and shoe how to construct and represent C-Surfaces and their intersection manifolds. A definition and new theoretical results are presented for a six-dimensional C-Space extension of the generalized Voronoi diagram, called the C-Voronoi diagram, whose structure we relate to the C-surface intersection manifolds. The representations and algorithms we develop impact many geometric planning problems, and extend to Cartesian manipulators with six degrees of freedom.