Navigation involves recognizing the environment, identifying the curre
nt position within the environment, and reaching particular positions.
We present a method for localization (the act of recognizing the envi
ronment), positioning (the act of computing the exact coordinates of a
robot in the environment), and homing (the act of returning to a prev
iously visited position) from visual input. The method is based on rep
resenting the scene as a set of 2D views and predicting the appearance
s of novel views by linear combinations of the model views. The method
accurately approximates the appearance of scenes under weak-perspecti
ve projection, Analysis of this projection as well as experimental res
ults demonstrate that in many cases this approximation is sufficient t
o accurately describe the scene. When weak-perspective approximation i
s invalid, either a larger number of models can be acquired or an iter
ative solution to account for the perspective distortions can be emplo
yed. The method has several advantages over other approaches. It uses
relatively rich representations; the representations are 2D rather tha
n 3D; and localization can be done from only a single 2D view without
calibration. The same principal method is applied for both the localiz
ation and positioning problems, and a simple ''qualitative'' algorithm
for homing is derived from this method.