Related papers: Local Morphometry of Closed, Implicit Surfaces

Knowledge of shape geometry plays a pivotal role in many shape analysis applications. In this paper we introduce a local geometry-inclusive global representation of 3D shapes based on computation of the shortest quasi-geodesic paths between…

For compression fracture detection and evaluation, an automatic X-ray image segmentation technique that combines deep-learning and level-set methods is proposed. Automatic segmentation is much more difficult for X-ray images than for CT or…

Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…

The Euler Characteristic Transform (ECT) of Turner et al. provides a way to statistically analyze non-diffeomorphic shapes without relying on landmarks. In applications, this transform is typically approximated by a discrete set of…

Morphological analysis of the left atrial appendage is an important tool to assess risk of ischemic stroke. Most deep learning approaches for 3D segmentation is guided by binary labelmaps, which results in voxelized segmentations unsuitable…

Over the past decade, lidars have become a cornerstone of robotics state estimation and perception thanks to their ability to provide accurate geometric information about their surroundings in the form of 3D scans. Unfortunately, most of…

We study a generalized boundary rigidity problem, which investigates whether the areas of embedded minimal surfaces can uniquely determine a Riemannian manifold with boundary. We prove that for a conformal perturbation of an analytic metric…

This paper presents a static electrical impedance tomography (EIT) technique that evaluates abdominal obesity by estimating the thickness of subcutaneous fat. EIT has a fundamental drawback for absolute admittivity imaging because of its…

In 1987, I. Labuda proved a general representation theorem that, as a special case, shows that the topology of local convergence in measure is the minimal topology on Orlicz spaces and $L_{\infty}$. Minimal topologies connect with the…

The aim of this paper is to investigate the differential geometry of immersed surfaces in three-dimensional normed spaces from the viewpoint of affine differential geometry. We endow the surface with a useful Riemannian metric which is…

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity…

We study sequences of conformal deformations of a smooth closed Riemannian manifold of dimension $n$, assuming uniform volume bounds and $L^{n/2}$ bounds on their scalar curvatures. Singularities may appear in the limit. Nevertheless, we…

We present a new method for visualizing implicit real algebraic curves inside a bounding box in the $2$-D or $3$-D ambient space based on numerical continuation and critical point methods. The underlying techniques work also for tracing…

The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…

A key technique of machine learning and computer vision is to embed discrete weighted graphs into continuous spaces for further downstream processing. Embedding discrete hierarchical structures in hyperbolic geometry has proven very…

We study generic conformally flat (analytic-)hypersurfaces in the Euclidean $4$-space $\mathbb{R}^4$. Such a local-hypersurface is obtained as an evolution of surfaces issuing from a certain surface in $\mathbb{R}^4$, and then, in…

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular…

We propose a fully unsupervised multi-modal deformable image registration method (UMDIR), which does not require any ground truth deformation fields or any aligned multi-modal image pairs during training. Multi-modal registration is a key…

In recent years, neural implicit representations have made remarkable progress in modeling of 3D shapes with arbitrary topology. In this work, we address two key limitations of such representations, in failing to capture local 3D geometric…

Deep learning-based medical image segmentation techniques have shown promising results when evaluated based on conventional metrics such as the Dice score or Intersection-over-Union. However, these fully automatic methods often fail to meet…