# Fundamental Limits in Multi-image Alignment

arXiv: https://arxiv.org/abs/1602.01541 · HTML: https://mlsanity.com/paper/1602.01541/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Feb 2016.

## Built on by (most cited first, 6 of 6)

- [Sensing Theorems for Unsupervised Learning in Linear Inverse Problems](https://mlsanity.com/paper/2203.12513/) (2022)
- [Bayesian Cram'er-Rao Bound Estimation with Score-Based Models](https://mlsanity.com/paper/2309.16076/) (2023)
- [Algorithms from Invariants: Smoothed Analysis of Orbit Recovery over SO(3)](https://mlsanity.com/paper/2106.02680/) (2021)
- [Multi-target detection with rotations](https://mlsanity.com/paper/2101.07709/) (2021)
- [Score-based diffusion priors for multi-target detection](https://mlsanity.com/paper/2312.08500/) (2023)
- [Fine Dense Alignment of Image Bursts through Camera Pose and Depth Estimation](https://mlsanity.com/paper/2312.05190/) (2023)

## Abstract (arXiv)

The performance of multi-image 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 multi-image 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 Cram'er-Rao and Ziv-Zakai lower bounds under different statistical models for the underlying image. The accuracy of the derived bounds is experimentally assessed through a comparison to the maximum likelihood estimator. 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. We find that increasing the number of images is only useful below a certain SNR threshold, above which the pairwise MLE estimation proves to be optimal. The analysis we present here brings further insight into the fundamental limitations of the multi-image alignment problem.