Panoramic image differences can be used for view-based homing under natural outdoor conditions, because they increase smoothly with distance from a reference location (Zeil et al., J Opt Soc Am A 20(3):450-469, 2003). The particular shape, slope and depth of such image difference functions (IDFs) recorded at any one place, however, depend on a number of factors that so far have only been qualitatively identified. Here we show how the shape of difference functions depends on the depth structure and the contrast of natural scenes, by quantifying the depth- distribution of different outdoor scenes and by comparing it to the difference functions calculated with differently processed panoramic images, which were recorded at the same locations. We find (1) that IDFs and catchment areas become systematically wider as the average distance of objects increases, (2) that simple image processing operations -- like subtracting the local mean, difference-of-Gaussian filtering and local contrast normalization -- make difference functions robust against changes in illumination and the spurious effects of shadows, and (3) by comparing depth-dependent translational and depth-independent rotational difference functions, we show that IDFs of contrast-normalized snapshots are predominantly determined by the depth-structure and possibly also by occluding contours in a scene. We propose a model for the shape of IDFs as a tool for quantitative comparisons between the shapes of these functions in different scenes.