Determining individual glomerular proteinuria and periglomerular infiltration in a cleared murine kidney by a 3-dimensional fast marching algorithm.

Three-dimensional (3D) imaging has advanced basic research and clinical medicine. However, limited resolution and imperfections of real-world 3D image material often preclude algorithmic image analysis. Here, we present a methodologic framework for such imaging and analysis for functional and spatial relations in experimental nephritis.

Image Morphing in Deep Feature Spaces: Theory and Applications.

This paper combines image metamorphosis with deep features. To this end, images are considered as maps into a high-dimensional feature space and a structure-sensitive, anisotropic flow regularization is incorporated in the metamorphosis model proposed by Miller and Younes (Int J Comput Vis 41(1):61-84, 2001) and Trouvé and Younes (Found Comput Math 5(2):173-198, 2005). For this model, a variational time discretization of the Riemannian path energy is presented and the existence of discrete geodesic paths minimizing this energy is demonstrated.

Statistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets.

Background: The efficient and robust statistical analysis of the shape of plant organs of different cultivars is an important investigation issue in plant breeding and enables a robust cultivar description within the breeding progress. Laserscanning is a highly accurate and high resolution technique to acquire the 3D shape of plant surfaces. The computation of a shape based principal component analysis (PCA) built on concepts from continuum mechanics has proven to be an effective tool for a qualitative and quantitative shape examination.

Joint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data.

Purpose: Cancers are almost always diagnosed by morphologic features in tissue sections. In this context, machine learning tools provide new opportunities to describe tumor immune cell interactions within the tumor microenvironment and thus provide phenotypic information that might be predictive for the response to immunotherapy.

Methods: We develop a machine learning approach using variational networks for joint image denoising and classification of tissue sections for melanoma, which is an established model tumor for immuno-oncology research.

Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies.

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets.

Functional Thin Films on Surfaces.

The motion of a thin viscous film of fluid on a curved surface exhibits many intricate visual phenomena, which are challenging to simulate using existing techniques. A possible alternative is to use a reduced model, involving only the temporal evolution of the mass density of the film on the surface. However, in this model, the motion is governed by a fourth-order nonlinear PDE, which involves geometric quantities such as the curvature of the underlying surface, and is therefore difficult to discretize.

Co-registration of intra-operative brain surface photographs and pre-operative MR images.

Purpose: Brain shift, the change in configuration of the brain after opening the dura mater, is a significant problem for neuronavigation. Brain structures at intra-operative deformed positions must be matched with corresponding structures in the pre-operative 3D planning data. A method to co-register the cortical surface from intra-operative microscope images with pre-operative MRI-segmented data was developed and tested.

Joint surface reconstruction and 4D deformation estimation from sparse data and prior knowledge for marker-less Respiratory motion tracking.

Purpose: The intraprocedural tracking of respiratory motion has the potential to substantially improve image-guided diagnosis and interventions. The authors have developed a sparse-to-dense registration approach that is capable of recovering the patient's external 3D body surface and estimating a 4D (3D + time) surface motion field from sparse sampling data and patient-specific prior shape knowledge.

Methods: The system utilizes an emerging marker-less and laser-based active triangulation (AT) sensor that delivers sparse but highly accurate 3D measurements in real-time.

Marker-less reconstruction of dense 4-D surface motion fields using active laser triangulation for respiratory motion management.

To manage respiratory motion in image-guided interventions a novel sparse-to-dense registration approach is presented. We apply an emerging laser-based active triangulation (AT) sensor that delivers sparse but highly accurate 3-D measurements in real-time. These sparse position measurements are registered with a dense reference surface extracted from planning data.

Restoring three-dimensional magnetic resonance angiography images with mean curvature motion.

Objective: The management of neurovascular disease requires precise information on the cerebral vascular anatomy. Digital subtraction angiography (DSA) is the gold standard against which other imaging modalities have to be measured. To improve the quality of three-dimensional (3D) magnetic resonance angiography (MRA) images, we present a novel concept in 3D image analysis.

Statistical osteoporosis models using composite finite elements: a parameter study.

Osteoporosis is a widely spread disease with severe consequences for patients and high costs for health care systems. The disease is characterised by a loss of bone mass which induces a loss of mechanical performance and structural integrity. It was found that transverse trabeculae are thinned and perforated while vertical trabeculae stay intact.

Mumford-Shah model for one-to-one edge matching.

This paper presents a new algorithm based on the Mumford-Shah model for simultaneously detecting the edge features of two images and jointly estimating a consistent set of transformations to match them. Compared to the current asymmetric methods in the literature, this fully symmetric method allows one to determine one-to-one correspondences between the edge features of two images. The entire variational model is realized in a multiscale framework of the finite element approximation.

Multiscale joint segmentation and registration of image morphology.

Multimodal image registration significantly benefits from previous denoising and structure segmentation and vice versa. In particular combined information of different image modalities makes segmentation significantly more robust. Indeed, fundamental tasks in image processing are highly interdependent.

An adaptive level set method for interactive segmentation of intracranial tumors.

Background: Meaningful segmentation of intracranial lesions can be of assistance for planning open navigated microneurosurgical procedures, as well as for radiotherapy. Meaningful segmentation, however, may be hampered by lack of computational power. The respective segmentation method should be based on state-of-the-art mathematical tools, and it should be suitable for real applications.

Robust feature detection and local classification for surfaces based on moment analysis.

The stable local classification of discrete surfaces with respect to features such as edges and corners or concave and convex regions, respectively, is as quite difficult as well as indispensable for many surface processing applications. Usually, the feature detection is done via a local curvature analysis. If concerned with large triangular and irregular grids, e.

Processing textured surfaces via anisotropic geometric diffusion.

A multiscale method in surface processing is presented which carries over image processing methodology based on nonlinear diffusion equations to the fairing of noisy, textured, parametric surfaces. The aim is to smooth noisy, triangulated surfaces and accompanying noisy textures-as they are delivered by new scanning technology-while enhancing geometric and texture features. For an initial textured surface a fairing method is described which simultaneously processes the texture and the surface.

A new software for prediction of femoral neck fractures.

Femoral neck fractures are an important clinical, social and economic problem. Even if many different attempts have been carried out to improve the accuracy predicting the fracture risk, it was demonstrated in retrospective studies that the standard clinical protocol achieves an accuracy of about 65%. A new procedure was developed including for the prediction not only bone mineral density but also geometric and femoral strength information and achieving an accuracy of about 80% in a previous retrospective study.

Exploring invariant sets and invariant measures.

We propose a method to explore invariant measures of dynamical systems. The method is based on numerical tools which directly compute invariant sets using a subdivision technique, and invariant measures by a discretization of the Frobenius-Perron operator. Appropriate visualization tools help to analyze the numerical results and to understand important aspects of the underlying dynamics.