Fundamental Limits in Multi-Image Alignment
The performance of multiimage alignment, bringing different images into one coordinate system, is critical in many applications with varied signal-to-noise ratio (SNR) conditions. A great amount of effort is being invested into developing methods to solve this problem. Several important questions thus arise, including: Which are the fundamental limits in multiimage alignment performance? Does having access to more images improve the alignment? Theoretical bounds provide a fundamental benchmark to compare methods and can help establish whether improvements can be made. In this work, we tackle the problem of finding the performance limits in image registration when multiple shifted and noisy observations are available. We derive and analyze the Cramér-Rao and Ziv-Zakai lower bounds under different statistical models for the underlying image. We show the existence of different behavior zones depending on the difficulty level of the problem, given by the SNR conditions of the input images. The analysis we present here brings further insight into the fundamental limitations of the multiimage alignment problem.