It is often necessary to identify a pattern of observed craters in a single
image of the lunar surface and without any prior knowledge of the camera's
location. This so-called "lost-in-space" crater identification problem is
common in both crater-based terrain relative navigation (TRN) and in automatic
registration of scientific imagery. Past work on crater identification has
largely been based on heuristic schemes, with poor performance outside of a
narrowly defined operating regime (e.g., nadir pointing images, small search
areas). This work provides the first mathematically rigorous treatment of the
general crater identification problem. It is shown when it is (and when it is
not) possible to recognize a pattern of elliptical crater rims in an image
formed by perspective projection. For the cases when it is possible to
recognize a pattern, descriptors are developed using invariant theory that
provably capture all of the viewpoint invariant information. These descriptors
may be pre-computed for known crater patterns and placed in a searchable index
for fast recognition. New techniques are also developed for computing pose from
crater rim observations and for evaluating crater rim correspondences. These
techniques are demonstrated on both synthetic and real images