# Variational Registration of Multiple Images with the SVD based SqN Distance Measure

## TL;DR

This paper introduces a novel image registration method for multiple images using the SVD-based SqN distance measure, demonstrating its superiority over existing approaches in various applications.

## Contribution

It proposes and evaluates the use of the Schatten q-norm based SqN distance for aligning multiple images, extending image registration techniques beyond two-image scenarios.

## Key findings

- SqN distance is effective for multiple image registration
- SqN outperforms competing methods in experiments
- Applicable to dynamic sequences and histological stacks

## Abstract

Image registration, especially the quantification of image similarity, is an important task in image processing. Various approaches for the comparison of two images are discussed in the literature. However, although most of these approaches perform very well in a two image scenario, an extension to a multiple images scenario deserves attention. In this article, we discuss and compare registration methods for multiple images. Our key assumption is, that information about the singular values of a feature matrix of images can be used for alignment. We introduce, discuss and relate three recent approaches from the literature: the Schatten q-norm based SqN distance measure, a rank based approach, and a feature volume based approach. We also present results for typical applications such as dynamic image sequences or stacks of histological sections. Our results indicate that the SqN approach is in fact a suitable distance measure for image registration. Moreover, our examples also indicate that the results obtained by SqN are superior to those obtained by its competitors.