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We consider the effect of exploration policy in the context of the autonomous construction of a visual map of an unknown environment. Like other concurrent mapping and localization (CML) tasks, odometric uncertainty poses the problem of introducing distortions into the map which are difficult to correct without costly on-line or post-processing algorithms. Our problem is further compounded by the implicit nature of the visual map representation, which is designed to accommodate a wide variety of visual phenomena without assuming a particular imaging platform, thereby precluding the inference of scene geometry. Such a representation presents a requirement for a relatively dense sampling of observations of the environment in order to produce reliable models. Our goal is to develop an online policy for exploring an unknown environment which minimizes map distortion while maximizing coverage. We do not depend on costly post-hoc expectation maximization approaches to improve the output, but rather employ extended Kalman filter (EKF) methods to localize each observation once, and rely on the exploration policy to ensure that sufficient information is available to localize the successive observations. We present an experimental analysis of a variety of exploratory policies, in both simulated and real environments, and demonstrate that with an effective policy an accurate map can be constructed.