A visual system is geometrically calibrated if its estimates of the spatial properties of a scene are accurate: straight lines are judged straight, angles are correctly estimated, and collinear line segments are perceived to fall on a common line. This paper describes two new calibration methods for a model visual system whose photoreceptors are initially at unknown locations. The methods can also compensate for optical distortions that are equivalent to remapping of receptor locations (e.g., spherical aberration). The methods work by comparing visual input across eye/head movements; they require no explicit feedback and no knowledge about the particular contents of a scene. This work has implications for development and calibration in biological visual systems.