Variational Registration of Multiple Images with the SVD Based SqN Distance Measure

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.