Related papers: Metrics, quantization and registration in varifold…
Graph isomorphism is an important problem as its worst-case time complexity is not yet fully understood. In this study, we try to draw parallels between a related optimization problem called point set registration. A graph can be…
We construct the differential geometry of smooth manifolds equipped with an algebraic curvature map acting as an area measure. Area metric geometry provides a spacetime structure suitable for the discussion of gauge theories and strings,…
In this paper, we seek to combine two emerging standpoints in control theory. On the one hand, recent advances in infinite-dimensional geometric control have unlocked a method for controlling (with arbitrary precision and in arbitrarily…
We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…
This paper introduces a new extension of Riemannian elastic curve matching to a general class of geometric structures, which we call (weighted) shape graphs, that allows for shape registration with partial matching constraints and…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies. We give estimates…
We present a simple geometric construction linking geometric to deformation quantization. Both theories depend on some apparently arbitrary parameters, most importantly a polarization and a symplectic connection, and for real polarizations…
Despite progress in the rapidly developing field of geometric deep learning, performing statistical analysis on geometric data--where each observation is a shape such as a curve, graph, or surface--remains challenging due to the…
A complete recipe of measure-preserving diffusions in Euclidean space was recently derived unifying several MCMC algorithms into a single framework. In this paper, we develop a geometric theory that improves and generalises this…
We study the problem of registering images. The framework we use is metamorphosis and we construct a variational Eulerian space-time setting and pose the registration problem as an infinite-dimensional optimisation problem. The geodesic…
We present a novel particle management method using the Characteristic Mapping framework. In the context of explicit evolution of parametrized curves and surfaces, the surface distribution of marker points created from sampling the…
The diffeomorphic registration framework enables to define an optimal matching function between two probability measures with respect to a data-fidelity loss function. The non convexity of the optimization problem renders the choice of this…
In formation control, an ensemble of autonomous agents is required to stabilize at a given configuration in the plane, doing so while agents are allowed to observe only a subset of the ensemble. As such, formation control provides a rich…
We propose an efficient framework for point cloud and measure registration using bi-Lipschitz homeomorphisms, achieving O(n log n) complexity, where n is the number of points. By leveraging the Energy-Distance (ED) kernel, which can be…
Surface metrology is the area of engineering concerned with the study of geometric variation in surfaces. This paper explores the potential for modern techniques from spatial statistics to act as generative models for geometric variation 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…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
This paper implements topology optimization on two-dimensional manifolds. In this paper, the material interpolation is implemented on a material parameter in the partial differential equation used to describe a physical field, when this…
We examine three-dimensional metric deformations based on a tetrad transformation through the action the matrices of scalar fields. We describe by this approach to deformation the results obtained by Coll et al. in [1], where it is stated…
Representing graphs as sets of node embeddings in certain curved Riemannian manifolds has recently gained momentum in machine learning due to their desirable geometric inductive biases, e.g., hierarchical structures benefit from hyperbolic…