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This paper presents an approach to building a map from a sparse set of noisy observations, taken from known locations by a sensor with no obvious geometric model. The basic approach is to fit an interpolant to the training data, representing the expected observation, and to assume additive sensor noise. This paper takes a Bayesian view of the problem, maintaining a posterior over interpolants rather than simply the maximum-likelihood interpolant, giving a measure of uncertainty in the map at any point. This is done using a Gaussian process (GP) framework. The approach is validated experimentally both in an indoor office environment and an outdoor urban environment, using observations from an omnidirectional camera mounted on a mobile robot. A set of training data is collected from each environment and processed offline to produce a GP model. The robot then uses that model to localize while traversing each environment.