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

Area of Science:

• Estimation Theory
• Image Processing
• Computational Imaging

Background:

• The Cramér-Rao lower bound (CRLB) quantifies estimation limits in imaging.
• Existing CRLB analyses often assume constant-variance noise, which is unrealistic for many applications.
• Signal-dependent noise and linear filtering effects on image registration CRLB are not well-established.

Purpose of the Study:

• To generalize image registration CRLB calculations for signal-dependent noise and linear filtering.
• To develop methods for creating radiometrically realistic simulated imagery for CRLB analysis.
• To optimize image-based tracker performance by selecting error-minimizing filters and integration times.

Main Methods:

• Developed computational methods to generalize CRLB calculations for rigid-translation estimation.
• Utilized computer animation software and optical properties databases for radiometric image simulations (DIRSIG).
• Derived generalized expressions for the rigid shift Fisher information matrix.

Main Results:

• Presented generalized CRLB expressions accounting for signal-dependent noise and linear filtering.
• Demonstrated the use of simulated imagery to select optimal filters and integration times for image-based trackers.
• Quantified the impact of filter-imposed noise correlation on registration error.

Conclusions:

• The generalized CRLB provides a more accurate assessment of fundamental limits for image registration under realistic noise conditions.
• Radiometrically realistic simulations are crucial for effective CRLB application in imaging system design.
• The developed methods aid in optimizing imaging system parameters for improved performance, especially with platform jitter.