Catchment areas of panoramic snapshots in outdoor scenes.

We took panoramic snapshots in outdoor scenes at regular intervals in two- or three-dimensional grids covering 1 m2 or 1 m3 and determined how the root mean square pixel differences between each of the images and a reference image acquired at one of the locations in the grid develop over distance from the reference position. We then asked whether the reference position can be pinpointed from a random starting position by moving the panoramic imaging device in such a way that the image differences relative to the reference image are minimized. We find that on time scales of minutes to hours, outdoor locations are accurately defined by a clear, sharp minimum in a smooth three-dimensional (3D) volume of image differences (the 3D difference function). 3D difference functions depend on the spatial-frequency content of natural scenes and on the spatial layout of objects therein. They become steeper in the vicinity of dominant objects. Their shape and smoothness, however, are affected by changes in illumination and shadows. The difference functions generated by rotation are similar in shape to those generated by translation, but their plateau values are higher. Rotational difference functions change little with distance from the reference location. Simple gradient descent methods are surprisingly successful in recovering a goal location, even if faced with transient changes in illumination. Our results show that view-based homing with panoramic images is in principle feasible in natural environments and does not require the identification of individual landmarks. We discuss the relevance of our findings to the study of robot and insect homing.