The problem that we wish to solve is that of obtaining a pose estimate for a robot located in a previously explored region of the environment. The robot is equipped with a single achromatic (grey scale) camera, and does not require an a priori estimate of its position. An accurate position estimate is desired without any motion on the part of the robot. One might imagine that the robot must consistently re-localise itself after periodic shutdowns for maintenance. We are also searching for a solution which is scalable, both in terms of the size of the environment, and the sampling density of the prior exploration, as well as robust to variations in lighting conditions. Finally, we are seeking a solution which permits accuracy to an arbitrary precision. We will evaluate the accuracy of a particular set of results with respect to the sampling density of the prior exploration, under the understanding that increased precision can be obtained by increasing the sampling density. The validity of this assumption will also be considered. In this thesis, we are concerned principally with experimental results. Theoretical issues are addressed with respect to their relevance to the method, and complexity issues are addressed in terms of both the computational and travel time required for exploration and subsequent position estimation. The accuracy of the results are considered under variations in environmental conditions in a variety of domains.