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Article
Open AccessGeometry of Needle-Like Microstructures in Shape-Memory Alloys
Needle-like microstructures are often observed in shape memory alloys near macro-interfaces that separate regions with different laminate orientation. We study their shape with a two-dimensional model based on...
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Article
Open AccessA pessimistic bilevel stochastic problem for elastic shape optimization
We consider pessimistic bilevel stochastic programs in which the follower maximizes over a fixed compact convex set a strictly convex quadratic function, whose Hessian depends on the leader’s decision. This re...
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Article
Open AccessConsistent Approximation of Interpolating Splines in Image Metamorphosis
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamo...
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Chapter and Conference Paper
The Variational Approach to the Flow of Sobolev-Diffeomorphisms Model
The flow of diffeomorphisms, aka LDDMM, is a framework to define a group G of diffeomorphisms of chosen regularity with a Riemannian structure. If these diffeomorphisms are used to deform a template shape or imag...
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Article
Open AccessImage 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 incorp...
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Chapter and Conference Paper
Splines for Image Metamorphosis
Cubic splines are a classical tool for higher order interpolation of points in Euclidean space known to minimize the integral of the squared acceleration along the interpolation path. This paper transfers this...
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Article
Open AccessStatistical shape analysis of tap roots: a methodological case study on laser scanned sugar beets
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 bree...
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Article
Computation of optimal transport on discrete metric measure spaces
In this paper we investigate the numerical approximation of an analogue of the Wasserstein distance for optimal transport on graphs that is defined via a discrete modification of the Benamou–Brenier formula. T...
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Article
Open AccessJoint reconstruction and classification of tumor cells and cell interactions in melanoma tissue sections with synthesized training data
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 mic...
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Chapter and Conference Paper
Time Discrete Geodesics in Deep Feature Spaces for Image Morphing
Image morphing in computer vision amounts to computing a visually ...
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Article
Open AccessShape-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 nonli...
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Chapter and Conference Paper
Variational Networks for Joint Image Reconstruction and Classification of Tumor Immune Cell Interactions in Melanoma Tissue Sections
Immunotherapy is currently revolutionizing the treatment of cancer. Detailed analyses of tumor immune cell interaction in the tumor microenvironment will facilitate an accurate prediction of a patient’s clinic...
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Chapter
Branching Structures in Elastic Shape Optimization
Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure...
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Chapter
Homogenization in Magnetic-Shape-Memory Polymer Composites
Magnetic-shape-memory materials (e.g. specific NiMnGa alloys) react with a large change of shape to the presence of an external magnetic field. As an alternative for the difficult to manufacture single crystal...
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Chapter and Conference Paper
GPU-Based Image Geodesics for Optical Coherence Tomography
Within a manifold framework, the interpolation of tomographic image time series is investigated. To this end, the metamorphosis model of a manifold of images is taken into account. Based on a variational time ...
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Chapter and Conference Paper
Transport Based Image Morphing with Intensity Modulation
We present a generalized optimal transport model in which the mass-preserving constraint for the \(L^2\) -Wa...
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Chapter and Conference Paper
Time Discrete Extrapolation in a Riemannian Space of Images
The Riemannian metamorphosis model introduced and analyzed in [7, 12] is taken into account to develop an image extrapolation tool in the space of images. To this end, the variational time discretization for the ...
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Chapter and Conference Paper
Bézier Curves in the Space of Images
Bézier curves are a widespread tool for the design of curves in Euclidian space. This paper generalizes the notion of Bézier curves to the infinite-dimensional space of images. To this end the space of images ...
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Reference Work Entry In depth
Variational Methods in Shape Analysis
The concept of a shape space is linked both to concepts from geometry and from physics. On one hand, a path-based viscous flow approach leads to Riemannian distances between shapes, where shapes are boundaries...
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Article
Co-registration of intra-operative brain surface photographs and pre-operative MR images
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 ...
