P. Whaite, F.P. Ferrie The bottom-up strategy often employed in building volumetric models of objects proceeds from the inference of parts to the estimation of part shape using an appropriate parametric model to describe each part. A principal weakness of this approach is that the resulting models are of limited stability, i.e. a small perturbation in the data can lead to large changes in the resulting model. We argue that this approach is inappropriate because the process of inference is inherently non-unique, i.e. the data cannot support the selection of one interpretation over another. It is therefore misleading to select an interpretation based on some ad-hoc criterion of ``perceptual acceptability'', but it is necessary to communicate the nature of the non-uniqueness to the processes that make use of the fitted models. The problem then is to devise the means by which to communicate the non-uniqueness. One possibility is to exploit the matrix of covariances produced as a by-product of the iterative fitting procedure. The covariance matrix describes an ellipsoid of confidence in parameter space, and the pose and shape of the ellipsoid captures the interdependencies of the parameter uncertainties. One way in which this measure of non-uniqueness can be exploited is in the selection of gaze positions for a mobile scanner. The idea is that the additional data obtained at the new position should maximize an improvement in the uniqueness of the volumetric interpretation. We have recently implemented this gaze control strategy in our autonomous exploration system and have shown that it can incrementally plan a scanning path so that data collected along the way results in a unique model in a time significantly faster than random probing.