Models of shape variations have become a central component for the automated analysis of images. An important class of shape models are point distribution models (PDMs). These models represent a class of shapes as a normal distribution of point variations, whose parameters are estimated from example shapes. Principal component analysis (PCA) is applied to obtain a low-dimensional representation of the shape variation in terms of the leading principal components. In this paper, we propose a generalization of PDMs, which we refer to as Gaussian Process Morphable Models (GPMMs). We model the shape variations with a Gaussian process, which we represent using the leading components of its Karhunen-Loève expansion. To compute the expansion, we make use of an approximation scheme based on the Nyström method. The resulting model can be seen as a continuous analog of a standard PDM. However, while for PDMs the shape variation is restricted to the linear span of the example data, with GPMMs we can define the shape variation using any Gaussian process. For example, we can build shape models that correspond to classical spline models and thus do not require any example data. Furthermore, Gaussian processes make it possible to combine different models. For example, a PDM can be extended with a spline model, to obtain a model that incorporates learned shape characteristics but is flexible enough to explain shapes that cannot be represented by the PDM. We introduce a simple algorithm for fitting a GPMM to a surface or image. This results in a non-rigid registration approach whose regularization properties are defined by a GPMM. We show how we can obtain different registration schemes, including methods for multi-scale or hybrid registration, by constructing an appropriate GPMM. As our approach strictly separates modeling from the fitting process, this is all achieved without changes to the fitting algorithm. To demonstrate the applicability and versatility of GPMMs, we perform a set of experiments in typical usage scenarios in medical image analysis and computer vision: The model-based segmentation of 3D forearm images and the building of a statistical model of the face. To complement the paper, we have made all our methods available as open source.

When used in combination with raster scanning, small-angle X-ray scattering (SAXS) has proven to be a valuable imaging technique of the nanoscale, for example of bone, teeth and brain matter. Although two-dimensional projection imaging has been used to characterize various materials successfully, its three-dimensional extension, SAXS computed tomography, poses substantial challenges, which have yet to be overcome. Previous work using SAXS computed tomography was unable to preserve oriented SAXS signals during reconstruction. Here we present a solution to this problem and obtain a complete SAXS computed tomography, which preserves oriented scattering information. By introducing virtual tomography axes, we take advantage of the two-dimensional SAXS information recorded on an area detector and use it to reconstruct the full three-dimensional scattering distribution in reciprocal space for each voxel of the three-dimensional object in real space. The presented method could be of interest for a combined six-dimensional real and reciprocal space characterization of mesoscopic materials with hierarchically structured features with length scales ranging from a few nanometres to a few millimetres--for example, biomaterials such as bone or teeth, or functional materials such as fuel-cell or battery components.

While large-scale synchrotron sources provide a highly brilliant monochromatic X-ray beam, these X-ray sources are expensive in terms of installation and maintenance, and require large amounts of space due to the size of storage rings for GeV electrons. On the other hand, laboratory X-ray tube sources can easily be implemented in laboratories or hospitals with comparatively little cost, but their performance features a lower brilliance and a polychromatic spectrum creates problems with beam hardening artifacts for imaging experiments. Over the last decade, compact synchrotron sources based on inverse Compton scattering have evolved as one of the most promising types of laboratory-scale X-ray sources: they provide a performance and brilliance that lie in between those of large-scale synchrotron sources and X-ray tube sources, with significantly reduced financial and spatial requirements. These sources produce X-rays through the collision of relativistic electrons with infrared laser photons. In this study, an analysis of the performance, such as X-ray flux, source size and spectra, of the first commercially sold compact light source, the Munich Compact Light Source, is presented.

Quite recently, a method has been presented to reconstruct X-ray scattering tensors from projections obtained in a grating interferometry setup. The original publications present a rather specialised approach, for instance by suggesting a single SART-based solver. In this work, we propose a novel approach to solving the inverse problem, allowing the use of other algorithms than SART (like conjugate gradient), a faster tensor recovery, and an intuitive visualisation. Furthermore, we introduce constraint enforcement for X-ray tensor tomography (cXTT) and demonstrate that this yields visually smoother results in comparison to the state-of-art approach, similar to regularisation.

Dual-energy CT has opened up a new level of quantitative X-ray imaging for many diagnostic applications. The energy dependence of the X-ray attenuation is the key to quantitative material decomposition of the volume under investigation. This material decomposition allows the calculation of virtual native images in contrast enhanced angiography, virtual monoenergetic images for beam-hardening artifact reduction and quantitative material maps, among others. These visualizations have been proven beneficial for various diagnostic questions. Here, we demonstrate a new method of ‘virtual dual-energy CT’ employing grating-based phase-contrast for quantitative material decomposition. Analogue to the measurement at two different energies, the applied phase-contrast measurement approach yields dual information in form of a phase-shift and an attenuation image. Based on these two image channels, all known dual-energy applications can be demonstrated with our technique. While still in a preclinical state, the method features the important advantages of direct access to the electron density via the phase image, simultaneous availability of the conventional attenuation image at the full energy spectrum and therefore inherently registered image channels. The transfer of this signal extraction approach to phase-contrast data multiplies the diagnostic information gained within a single CT acquisition. The method is demonstrated with a phantom consisting of exemplary solid and fluid materials as well as a chicken heart with an iodine filled tube simulating a vessel. For this first demonstration all measurements have been conducted at a compact laser-undulator synchrotron X-ray source with a tunable X-ray energy and a narrow spectral bandwidth, to validate the quantitativeness of the processing approach.