Related papers: Medial Axis Isoperimetric Profiles

Real-world data typically contain repeated and periodic patterns. This suggests that they can be effectively represented and compressed using only a few coefficients of an appropriate basis (e.g., Fourier, Wavelets, etc.). However, distance…

Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…

For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal partitioning of the domain. Similarly to other multiscale…

We propose a numerical method for the solution of electromagnetic problems on axisymmetric domains, based on a combination of a spectral Fourier approximation in the azimuthal direction with an IsoGeometric Analysis (IGA) approach in the…

We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in…

For a given planar convex compact set $K$, consider a bisection $\{A,B\}$ of $K$ (i.e., $A\cup B=K$ and whose common boundary $A\cap B$ is an injective continuous curve connecting two boundary points of $K$) minimizing the corresponding…

We obtain an explicit uniform upper bound for the derivative of a conformal mapping of the unit disk onto a convex domain. This estimate depends only on the outer and inner radii of the domain, and on a curvature radius of its boundary. Its…

Motivated by the fact that the medial axis transform is able to encode nearly the complete shape, we propose to use as few medial balls as possible to approximate the original enclosed volume by the boundary surface. We progressively select…

This paper presents a PDE-based parameterisation framework for addressing the planar surface-to-volume (StV) problem of finding a valid description of the domain's interior given no more than a spline-based description of its boundary…

Conformal Prediction methods have finite-sample distribution-free marginal coverage guarantees. However, they generally do not offer conditional coverage guarantees, which can be important for high-stakes decisions. In this paper, we…

We present a new and direct proof of the local Neumann isoperimetric inequality on convex domains of a Riemannian manifold with Ricci curvature bounded below.

Surface analysis of the cortex is ubiquitous in human neuroimaging with MRI, e.g., for cortical registration, parcellation, or thickness estimation. The convoluted cortical geometry requires isotropic scans (e.g., 1mm MPRAGEs) and good…

Shape reconstruction from imaging volumes is a recurring need in medical image analysis. Common workflows start with a segmentation step, followed by careful post-processing and,finally, ad hoc meshing algorithms. As this sequence can be…

Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…

We solve the problem of best approximation by partial isometries of given rank to an arbitrary rectangular matrix, when the distance is measured in any unitarily invariant norm. In the case where the norm is strictly convex, we parametrize…

Persistence diagrams are common descriptors of the topological structure of data appearing in various classification and regression tasks. They can be generalized to Radon measures supported on the birth-death plane and endowed with an…

Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standard isogeometric discretizations require a global…

The objective of this research is the development of a geometrically exact model for the analysis of arbitrarily curved spatial Bernoulli-Euler beams. The complete metric of the beam is utilized in order to include the effect of curviness…

Local alignment between medical images and text is essential for accurate diagnosis, though it remains challenging due to the absence of natural local pairings and the limitations of rigid region recognition methods. Traditional approaches…