Fundamental performance limits in image registration

While many algorithms have been developed to solve the problem of image registration, their performance has typically been evaluated only by comparing one method with another often in an ad-hoc manner. We propose a statistical performance measure based on the mean square error (MSE) and explore the performance bounds using the Cramer-Rao inequality. We show how these performance bounds depend on image content under observation. By analyzing these bounds we provide insight into the inherent tradeoff between bias and variance found in all image registration algorithms. Specifically, we derive a functional expression for the bias inherent in the popular class of gradient-based image registration algorithms.