Related papers: Shape analysis via gradient flows on diffeomorphis…
Shaping of magnetic flux surfaces is found to have a strong impact on turbulence and transport in tokamak edge plasmas. A series of axisymmetric equilibria with varying elongation and triangularity, and a divertor configuration are…
The shearlet transform from applied harmonic analysis is currently the state of the art when analyzing multidimensional signals with anisotropic singularities. Its optimal sparse approximation properties and its faithful digitalization…
In computational anatomy, the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework has become a central tool for modeling smooth, invertible transformations between shapes such as curves or landmarks. In this paper, we extend…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
We study a Dirichlet problem for the heat equation in a domain containing an interior hole. The domain has a fixed outer boundary and a variable inner boundary determined by a diffeomorphism $\phi$. We analyze the maps that assign to the…
We introduce a latent 3D representation that models 3D surfaces as probability density functions in 3D, i.e., p(x,y,z), with flow-matching. Our representation is specifically designed for consumption by machine learning models, offering…
Wavefront shaping is a technique to study and control light transport inside scattering media. Wavefront shaping is considered to be applicable to any complex material, yet in most previous studies, the only sample geometries that are…
The task of shape abstraction with semantic part consistency is challenging due to the complex geometries of natural objects. Recent methods learn to represent an object shape using a set of simple primitives to fit the target.…
We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $\Lambda_{A}$ of the substrate is…
In this article we introduce a diffeomorphism-invariant Riemannian metric on the space of vector valued one-forms. The particular choice of metric is motivated by potential future applications in the field of functional data and shape…
Computational design optimization in fluid dynamics usually requires to solve non-linear partial differential equations numerically. In this work, we explore a Bayesian optimization approach to minimize an object's drag coefficient in…
We describe a diffeomorphic registration algorithm that allows groups of images to be accurately aligned to a common space, which we intend to incorporate into the SPM software. The idea is to perform inference in a probabilistic graphical…
Deep generative models learn the data distribution, which is concentrated on a low-dimensional manifold. The geometric analysis of distribution transformation provides a better understanding of data structure and enables a variety of…
In this paper, we propose a transformer-based procedure for the efficient registration of non-rigid 3D point clouds. The proposed approach is data-driven and adopts for the first time the transformer architecture in the registration task.…
Diffusion models, while trained for image generation, have emerged as powerful foundational feature extractors for downstream tasks. We find that off-the-shelf diffusion models, trained exclusively to generate natural RGB images, can…
In this work, we propose a novel technique to generate shapes from point cloud data. A point cloud can be viewed as samples from a distribution of 3D points whose density is concentrated near the surface of the shape. Point cloud generation…
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…
Body reshaping is an important procedure in portrait photo retouching. Due to the complicated structure and multifarious appearance of human bodies, existing methods either fall back on the 3D domain via body morphable model or resort to…
For addressing optimisation tasks on finite dimensional quantum systems, we give a comprehensive account of the foundations of gradient flows on Riemannian manifolds including new developments: we extend former results from Lie groups such…
In machine learning and neuroscience, certain computational structures and algorithms are known to yield disentangled representations without us understanding why, the most striking examples being perhaps convolutional neural networks and…