Robust estimation of structure from motion in the uncalibrated case

Abstract

A picture of a scene is a 2-dimensional representation of a 3-dimensional world. In the process of projecting the scene onto the 2-dimensional image plane, some of the information about the 3-dimensional scene is inevitably lost. Given a series of images of a scene, typically taken by a video camera, it is sometimes possible to recover some of this lost 3-dimensional information. Within the computer vision literature this process is described as that of recovering structure from motion. If some of the information about the internal geometry of the camera is unknown, then the problem is described as that of recovering structure from motion in the uncalibrated case. It is this uncalibrated version of the problem that is the concern of this thesis. Optical flow represents the movement of points across the image plane over time. Previous work in the area of structure from motion has given rise to a so-called differential epipolar equation which describes the relationship between optical flow and the motion and internal parameters of the camera. This equation allows the calibration of a camera undergoing unknown motion and having an unknown, and possibly varying, focal length. Obtaining accurate estimates of the camera motion and internal parameters in the presence of noisy optical flow data is critical to the structure recovery process. We present and compare a variety of methods for estimating the coefficients of the differential epipolar equation. The goal of this process is to derive a tractable total least squares estimator of structure from motion robust to the presence of inaccuracies in the data. Methods are also presented for rectifying optical flow to a particular motion estimates, eliminating outliers from the data, and calculating the relative motion of a camera over an image sequence. This thesis thus explores the application of numerical and statistical techniques for the estimation of structure from motion in the uncalibrated case.