Cramér-Rao lower bound calculations for image registration using simulated phenomenology

The Cramér-Rao lower bound (CRLB) is a valuable tool to quantify fundamental limits to estimation problems associated with imaging systems, and has been used previously to study image registration performance bounds. Most existing work, however, assumes constant-variance noise; for many applications, noise is signal-dependent. Further, linear filters applied after detection can potentially yield reduced registration error, but prior work has not treated the CRLB behavior caused by filter-imposed noise correlation. We have developed computational methods to efficiently generalize existing image registration CRLB calculations to account for the effect of both signal-dependent noise and linear filtering on the estimation of rigid-translation ("shift") parameters. Because effective use of the CRLB requires radiometrically realistic simulated imagery, we have also developed methods to exploit computer animation software and available optical properties databases to conveniently build and modify synthetic objects for radiometric image simulations using DIRSIG. In this paper, we present the generalized expressions for the rigid shift Fisher information matrix and discuss the properties of the associated CRLB. We discuss the methods used to synthesize object "sets" for use in DIRSIG, and then demonstrate the use of simulated imagery in the CRLB code to choose an error-minimizing filter and optimal integration time for an image-based tracker in the presence of random platform jitter.