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.

The comparison of images is an important task in image processing. For a comparison of two images, a variety of measures has been suggested. However, applications such as dynamic imaging or serial sectioning provide a series of many images to be compared. When these images are to be registered, the standard approach is to sequentially align the j-th image with respect to its neighbours and sweep with respect to j. One of the disadvantages is that information is distributed only locally.We introduce an alternative so-called SqN approach. SqN is based on the Schatten-q-norm of the image sequence gradients, i.e. rank information of image gradients of the whole image sequence. With this approach, information is transported globally. Our experiments show that SqN gives at least comparable registration results to standard distance measures but its computation is about six times faster.

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.

Purpose: Biopsies are a diagnostic tool for the diagnosis of histopathological, molecular biological, proteomic, and imaging data, to narrow down disease patterns or identify diseases. Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) provides an emerging state-of-the-art technique for molecular imaging of biological tissue. The aim of this study is the registration of MALDI MSI data sets and data acquired from different histological stainings to create a 3D model of biopsies and whole organs. Experimental design: The registration of the image modalities is achieved by using a variant of the authors' global, deformable Schatten-q-Norm registration approach. Utilizing a connected-component segmentation for background removal followed by a principal-axis based linear pre-registration, the images are adjusted into a homogeneous alignment. This registration approach is accompanied by the 3D reconstruction of histological and MALDI MSI data. Results: With this, a system of automatic registration for cross-process evaluation, as well as for creating 3D models, is developed and established. The registration of MALDI MSI data with different histological image data is evaluated by using the established global image registration system. Conclusions and clinical relevance: In conclusion, this multimodal image approach offers the possibility of molecular analyses of tissue specimens in clinical research and diagnosis.

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