Related papers: Local Morphometry of Closed, Implicit Surfaces

Ultrasound (US) imaging is increasingly used in spinal procedures due to its real-time, radiation-free capabilities; however, its effectiveness is hindered by shadowing artifacts that obscure deeper tissue structures. Traditional…

This paper presents a LiDAR odometry estimation framework called Generalized LOAM. Our proposed method is generalized in that it can seamlessly fuse various local geometric shapes around points to improve the position estimation accuracy…

We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…

It is challenging to directly estimate the human geometry from a single image due to the high diversity and complexity of body shapes with the various clothing styles. Most of model-based approaches are limited to predict the shape and pose…

We introduce an orientation-preserving landmark-based distance for continuous curves, which can be viewed as an alternative to the \Frechet or Dynamic Time Warping distances. This measure retains many of the properties of those measures,…

Collision detection is one of the most time-consuming operations during motion planning. Thus, there is an increasing interest in exploring machine learning techniques to speed up collision detection and sampling-based motion planning. A…

We consider the problem of prescribing the Gaussian and the geodesic curvatures of a compact surface with boundary by a conformal deformation of the metric. We derive some existence results using a variational approach, either by…

Accurate 3D models of the human heart require not only correct outer surfaces but also realistic inner structures, such as the ventricles, atria, and myocardial layers. Approaches relying on implicit surfaces, such as signed distance…

Signed Distance Functions (SDFs) are vital implicit representations to represent high fidelity 3D surfaces. Current methods mainly leverage a neural network to learn an SDF from various supervisions including signed distances, 3D point…

Regularization strategies in medical image registration often take a one-size-fits-all approach by imposing uniform constraints across the entire image domain. Yet biological structures are anything but regular. Lacking structural…

Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most…

The level-set method is a popular interface tracking method in two-phase flow simulations. An often-cited reason for using it is that the method naturally handles topological changes in the interface, e.g. merging drops, due to the implicit…

Overparameterized shallow neural networks admit substantial parameter redundancy: distinct parameter vectors may represent the same predictor due to hidden-unit permutations, rescalings, and related symmetries. As a result, geometric…

Purpose: Intraoperative ultrasound scanning is a demanding visuotactile task. It requires operators to simultaneously localise the ultrasound perspective and manually perform slight adjustments to the pose of the probe, making sure not to…

Nonlinear dimensionality reduction techniques, particularly UMAP, are widely used for visualizing high-dimensional data. However, UMAP's local Euclidean distance assumption often fails to capture intrinsic manifold geometry, leading to…

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…

The isometric immersion of two-dimensional Riemannian manifolds or surfaces with negative Gauss curvature into the three-dimensional Euclidean space is studied in this paper. The global weak solutions to the Gauss-Codazzi equations with…

Maintaining stable and accurate localization during fast motion or on rough terrain remains highly challenging for mobile robots with onboard resources. Currently, multi-sensor fusion methods based on continuous-time representation offer a…

To what extent are two images picturing the same 3D surfaces? Even when this is a known scene, the answer typically requires an expensive search across scale space, with matching and geometric verification of large sets of local features.…

We determine the local geometric structure of two-dimensional metric spaces with curvature bounded above as the union of finitely many properly embedded/branched immersed Lipschitz disks. As a result, we obtain a graph structure of the…