Abstract: A similarity-based database of images, where images are preferably ranked and correlated in correspondence to biological preattentive similarity, supports a new type of interface for visual navigation within the database to the end that a human may perceive not only selected images resultant from a query, but the relationship between the selected images. In particular, navigation is within a display space whose geometric characteristics depend on the geometry of the perceptual space in which image similarity is measured. The display space is a subset of the three dimensional Euclidean space that, for many of the distance functions appropriate to the images, is contained in the unit cube. The perceptual intuition of the metric is given (i) in part by the distribution of images in the space, and (ii) in part by making the motion of the user uniform with respect to the metric of the space.