Related papers: Local Morphometry of Closed, Implicit Surfaces

We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the…

In this paper, we propose a method to represent a fingerprint image by an ordered, fixed-length bit-string providing improved accuracy performance, faster matching time and compressibility. First, we devise a novel minutia-based local…

In this work, based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary. For boundary with simple geometry, we theoretically analyse…

Graph embeddings have become a key and widely used technique within the field of graph mining, proving to be successful across a broad range of domains including social, citation, transportation and biological. Graph embedding techniques…

There are two main approaches to building locally flat embedded surfaces in 4-manifolds: direct methods which geometrically manipulate a given map of a surface, and more indirect methods using surgery theory. Both rely on Freedman-Quinn's…

Medical ultrasound (US) imaging is a frontline tool for the diagnosis of kidney diseases. However, traditional freehand imaging procedure suffers from inconsistent, operator-dependent outcomes, lack of 3D localization information, and risks…

In this paper we propose a new analytical preintegration theory for graph-based sensor fusion with an inertial measurement unit (IMU) and a camera (or other aiding sensors).Rather than using discrete sampling of the measurement dynamics as…

Image registration is a fundamental task in medical image analysis. Deformations are often closely related to the morphological characteristics of tissues, making accurate feature extraction crucial. Recent weakly supervised methods improve…

Local covariance structure under the manifold setup has been widely applied in the machine learning society. Based on the established theoretical results, we provide an extensive study of two relevant manifold learning algorithms, empirical…

In this article, we study a free boundary isometric embedding problem for abstract Riemannian two-manifolds with the topology of the disc. Under the assumption of positive Gauss curvature and geodesic curvature of the boundary being equal…

We propose an immersed boundary scheme for the numerical resolution of the Complete Electrode Model in Electrical Impedance Tomography, that we use as a main ingredient in the resolution of inverse problems in medical imaging. Such method…

In this paper we find strictly locally convex hypersurfaces in $\mathbb{R}^{n+1}$ with prescribed curvature and boundary. The main result is that if the given data admits a strictly locally convex radial graph as a subsolution, we can find…

\textit{Implicit neural representations} (INRs) have emerged as a promising framework for representing signals in low-dimensional spaces. This survey reviews the existing literature on the specialized INR problem of approximating…

A novel algorithm is proposed for quantitative comparisons between compact surfaces embedded in the three-dimensional Euclidian space. The key idea is to identify those objects with the associated surface measures and compute a weak…

This preliminary report studies immersed surfaces of constant mean curvature in $H^3$ through their {\it adjusted Gauss maps} (as harmonic maps in $S^2$) and their {\it adjusted frames} in SU(2). Lawson's correspondence between Euclidean…

This paper develops a deformation-field geometry for spaces whose local frames may undergo internal stretching, compression, and shear. Ordinary Riemannian geometry takes an intrinsic metric geometry \((M,g)\) as the given datum and uses…

In motion analysis and understanding it is important to be able to fit a suitable model or structure to the temporal series of observed data, in order to describe motion patterns in a compact way, and to discriminate between them. In an…

Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…

Whereas dedicated scene representations are required for each different task in conventional robotic systems, this paper demonstrates that a unified representation can be used directly for multiple key tasks. We propose the Log-Gaussian…

Accurate 3D reconstruction of vertebral anatomy from ultrasound is important for guiding minimally invasive spine interventions, but it remains challenging due to acoustic shadowing and view-dependent signal variations. We propose an…