Related papers: Extracting Manifold Information from Point Clouds

We introduce a continuous domain framework for the recovery of points on a surface in high dimensional space, represented as the zero-level set of a bandlimited function. We show that the exponential maps of the points on the surface…

This research uses deep learning to estimate the topology of manifolds represented by sparse, unordered point cloud scenes in 3D. A new labelled dataset was synthesised to train neural networks and evaluate their ability to estimate the…

We present multiresolution tree-structured networks to process point clouds for 3D shape understanding and generation tasks. Our network represents a 3D shape as a set of locality-preserving 1D ordered list of points at multiple…

We propose a level set method to reconstruct unknown surfaces from point clouds, without assuming that the connections between points are known. We consider a variational formulation with a curvature constraint that minimizes the surface…

Characterizing microstructure-material-property relations calls for software tools which extract point-cloud- and continuum-scale-based representations of microstructural objects. Application examples include atom probe, electron, and…

A recent paper (Neural Networks, {\bf 132} (2020), 253-268) introduces a straightforward and simple kernel based approximation for manifold learning that does not require the knowledge of anything about the manifold, except for its…

This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…

Point normal, as an intrinsic geometric property of 3D objects, not only serves conventional geometric tasks such as surface consolidation and reconstruction, but also facilitates cutting-edge learning-based techniques for shape analysis…

In healthcare, accurately classifying medical images is vital, but conventional methods often hinge on medical data with a consistent grid structure, which may restrict their overall performance. Recent medical research has been focused on…

Point clouds are often sparse and incomplete, which imposes difficulties for real-world applications. Existing shape completion methods tend to generate rough shapes without fine-grained details. Considering this, we introduce a two-branch…

Partial differential equations (PDE) on manifolds arise in many areas, including mathematics and many applied fields. Among all kinds of PDEs, the Poisson-type equations including the standard Poisson equation and the related eigenproblem…

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space…

A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…

The points on the point clouds that can entirely outline the shape of the model are of critical importance, as they serve as the foundation for numerous point cloud processing tasks and are widely utilized in computer graphics and…

We study the problem of the appropriate choice of the interpolating kernel to be used in the evaluation of gradients of functions. Such interpolation technique is often used in applications, e.g. it is typical for Smoothed Particle…

Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, 3D object analysis. This paper studies the…

This paper presents an end-to-end differentiable algorithm for robust and detail-preserving surface normal estimation on unstructured point-clouds. We utilize graph neural networks to iteratively parameterize an adaptive anisotropic kernel…

As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…

The analyses relying on 3D point clouds are an utterly complex task, often involving million of points, but also requiring computationally efficient algorithms because of many real-time applications; e.g. autonomous vehicle. However, point…

Motivation: Assessing the match between two biomolecular structures is at the heart of structural analyses such as superposition, alignment and docking. These tasks are typically solved with specialized structure-matching techniques…