Learning Object-Independent Modes of Variation with Feature Flow Fields

We present a unifying framework in which "object-independent" modes of variation are learned from continuous-time data such as video sequences. These modes of variation can be used as "generators" to produce a manifold of images of a new object from a single example of that object. We develop the framework in the context of a well-known example: analyzing the modes of spatial deformations of a scene under camera movement. Our method learns a close approximation to the standard affine deformations that are expected from the geometry of the situation, and does so in a completely unsupervised (i.e. ignorant of the geometry of the situation) fashion. We stress that it is learning a "parameterization", not just the parameter values, of the data. We then demonstrate how we have used the same framework to derive a novel data-driven model of joint color change in images due to common lighting variations. The model is superior to previous models of color change in describing non-linear color changes due to lighting.

Swimming in Space-Time

Cyclic changes in the shape of a quasi-rigid body on a curved manifold can lead to net translation and/or rotation of the body in the manifold. Presuming space-time is a curved manifold as portrayed by general relativity, translation in space can be accomplished simply by cyclic changes in the shape of a body, without any thrust or external forces.

Light Field Morphable Models

Statistical shape and texture appearance models are powerful image representations, but previously had been restricted to 2D or simple 3D shapes. In this paper we present a novel 3D morphable model based on image-based rendering techniques, which can represent complex lighting conditions, structures, and surfaces. We describe how to construct a manifold of the multi-view appearance of an object class using light fields and show how to match a 2D image of an object to a point on this manifold. In turn we use the reconstructed light field to render novel views of the object. Our technique overcomes the limitations of polygon based appearance models and uses light fields that are acquired in real-time.

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.

Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming

We study the preconditioning of symmetric indefinite linear systems of equations that arise in interior point solution of linear optimization problems. The preconditioning method that we study exploits the block structure of the augmented matrix to design a similar block structure preconditioner to improve the spectral properties of the resulting preconditioned matrix so as to improve the convergence rate of the iterative solution of the system. We also propose a two-phase algorithm that takes advantage of the spectral properties of the transformed matrix to solve for the Newton directions in the interior-point method. Numerical experiments have been performed on some LP test problems in the NETLIB suite to demonstrate the potential of the preconditioning method discussed.