Towards an estimation framework for some problems in computer vision.

Abstract

This thesis is concerned with fundamental algorithms for estimating parameters of geometric models that are particularly relevant to computer vision. A general framework is considered which accommodates several important problems involving estimation in a maximum likelihood setting. By considering a special form of a commonly used cost function, a new, iterative, estimation method is evolved. This method is subsequently expanded to enable incorporation of a so-called ancillary constraint. An important feature of these methods is that they can serve as a basis for conducting theoretical comparison of various estimation approaches. Two specific applications are considered: conic fitting, and estimation of the fundamental matrix (a matrix arising in stereo vision). In the case of conic fitting, unconstrained methods are first treated. The problem of producing ellipse-specific estimates is subsequently tackled. For the problem of estimating the fundamental matrix, the new constrained method is applied to generate an estimate which satisfies the necessary rank-two constraint. Other constrained and unconstrained methods are compared within this context. For both of these example problems, the unconstrained and constrained methods are shown to perform with high accuracy and efficiency. The value of incorporating covariance information characterising the uncertainty of measured image point locations within the estimation process is also explored. Covariance matrices associated with data points are modelled, then an empirical study is made of the conditions under which covariance information enables generation of improved parameter estimates. Under the assumption that covariance information is, in itself, subject to estimation error, tests are undertaken to determine the effect of imprecise information upon the quality of parameter estimates. Finally, these results are carried over to experiments to assess the value of covariance information in estimating the fundamental matrix from real images. The use of such information is shown to be of potential benefit when the measurement process of image features is considered.