# Universal Joint Image Clustering and Registration using Partition Information

## TL;DR

This paper introduces a unified approach for joint image clustering and registration using multivariate information functionals, demonstrating asymptotic optimality and consistency in various multi-image scenarios.

## Contribution

It proposes novel algorithms based on multivariate information functionals for joint clustering and registration, with proven asymptotic optimality and consistency.

## Key findings

- Maximum mutual information achieves asymptotic optimality in two-image registration.
- Multiinformation-based algorithms outperform pairwise methods in multi-image registration.
- Algorithms are order-optimal for large-scale image clustering and registration.

## Abstract

We consider the problem of universal joint clustering and registration of images and define algorithms using multivariate information functionals. We first study registering two images using maximum mutual information and prove its asymptotic optimality. We then show the shortcomings of pairwise registration in multi-image registration, and design an asymptotically optimal algorithm based on multiinformation. Further, we define a novel multivariate information functional to perform joint clustering and registration of images, and prove consistency of the algorithm. Finally, we consider registration and clustering of numerous limited-resolution images, defining algorithms that are order-optimal in scaling of number of pixels in each image with the number of images.