# A Novel Similarity Measure for Image Sequences

## TL;DR

This paper introduces a new global similarity measure for image sequences based on Schatten-q-norms of gradient matrices, enabling unbiased registration of dynamic and serial images with promising initial results.

## Contribution

It proposes a novel similarity measure that considers all images simultaneously, improving registration accuracy for sequences and serial sections.

## Key findings

- Effective registration of DCE-MRI sequences demonstrated.
- Successful serial section alignment shown in experiments.
- Preservation of global data structure in registration results.

## Abstract

Quantification of image similarity is a common problem in image processing. For pairs of two images, a variety of options is available and well-understood. However, some applications such as dynamic imaging or serial sectioning involve the analysis of image sequences and thus require a simultaneous and unbiased comparison of many images. This paper proposes a new similarity measure, that takes a global perspective and involves all images at the same time. The key idea is to look at Schatten-q-norms of a matrix assembled from normalized gradient fields of the image sequence. In particular, for q = 0, the measure is minimized if the gradient information from the image sequence has a low rank. This global perspective of the novel SqN-measure does not only allow to register sequences from dynamic imaging, e.g. DCE-MRI, but is also a new opportunity to simultaneously register serial sections, e.g. in histology. In this way, an accumulation of small, local registration errors may be avoided. First numerical experiments show very promising results for a DCE-MRI sequence of a human kidney as well as for a set of serial sections. The global structure of the data used for registration with SqN is preserved in all cases.