相关论文: Local Morphometry of Closed, Implicit Surfaces

We survey recent results in hermitian integral geometry, i.e. integral geometry on complex vector spaces and complex space forms. We study valuations and curvature measures on complex space forms and describe how the global and local…

Variational analysis presents a unified theory encompassing in particular both smoothness and convexity. In a Euclidean space, convex sets and smooth manifolds both have straightforward local geometry. However, in the most basic hybrid case…

The purpose of this paper is to help the anesthesiologist to find the epidural depth automatically to make the first attempt to enter the path of the needle into the patient's body while it is clogged with bone and avoid causing a puncture…

In this paper, a multi-scale framework with local region based active contour and boundary shape similarity constraint is proposed for the segmentation of levator hiatus in ultrasound images. In this paper, we proposed a multiscale active…

Geometric embeddings have recently received attention for their natural ability to represent transitive asymmetric relations via containment. Box embeddings, where objects are represented by n-dimensional hyperrectangles, are a particularly…

This paper deals with two related problems, namely distance-preserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset $\mathcal{X} \subset \mathbb{R}^n$, associated…

Ultrasound offers a radiation-free, cost-effective solution for real-time visualization of spinal landmarks, paraspinal soft tissues and neurovascular structures, making it valuable for intraoperative guidance during spinal procedures.…

Longitudinal image registration enables studying temporal changes in brain morphology which is useful in applications where monitoring the growth or atrophy of specific structures is important. However this task is challenging due to;…

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary…

We present a novel Eulerian meshless method for two-phase flows with arbitrary embedded geometries. The spatial derivatives are computed using the meshless generalized finite difference method (GFDM). The sharp phase interface is tracked…

In this paper, we study the smooth isometric immersion of a complete, simply connected surface with a negative Gauss curvature into the three-dimensional Euclidean space. A fundamental and longstanding problem is to find a sufficient…

Recent research on graph embedding has achieved success in various applications. Most graph embedding methods preserve the proximity in a graph into a manifold in an embedding space. We argue an important but neglected problem about this…

Modeling scene geometry using implicit neural representation has revealed its advantages in accuracy, flexibility, and low memory usage. Previous approaches have demonstrated impressive results using color or depth images but still have…

Dynamic MRI may capture temporal anatomical changes in soft tissue organs with high contrast but the obtained sequences usually suffer from limited volume coverage which makes the high resolution reconstruction of organ shape trajectories a…

For a large class of metric spaces with nice local structure, which includes Banach-Finsler manifolds and geodesic spaces of curvature bounded above, we give sufficient conditions for a local homeomorphism to be a covering projection. We…

We show that for a very general class of curvature functions defined in the positive cone, the problem of finding a complete strictly locally convex hypersurface in $H^n+1$ satisfying $f(\kappa)=\sigma\in(0, 1)$ with a prescribed asymptotic…

Families of conformal field theories are naturally endowed with a Riemannian geometry which is locally encoded by correlation functions of exactly marginal operators. We show that the curvature of such conformal manifolds can be computed…

This article derives closed-form parametric formulas for the Minkowski sums of convex bodies in d-dimensional Euclidean space with boundaries that are smooth and have all positive sectional curvatures at every point. Under these conditions,…

We examine the space of surfaces in $\RR^{3}$ which are complete, properly embedded and have nonzero constant mean curvature. These surfaces are noncompact provided we exclude the case of the round sphere. We prove that the space $\Mk$ of…

Valuations constitute a class of functionals on convex bodies which include the Euler-characteristic, the surface area, the Lebesgue-measure, and many more classical functionals. Curvature measures may be regarded as "localised`` versions…