Related papers: PoNQ: a Neural QEM-based Mesh Representation

Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…

Ground-state 3D geometries of molecules are essential for many molecular analysis tasks. Modern quantum mechanical methods can compute accurate 3D geometries but are computationally prohibitive. Currently, an efficient alternative to…

We present a self-supervised learning approach to learning monocular 3D face reconstruction with a pose guidance network (PGN). First, we unveil the bottleneck of pose estimation in prior parametric 3D face learning methods, and propose to…

This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simplicial complexes, we capture not only adjacency relationships…

Few prior works study deep learning on point sets. PointNet by Qi et al. is a pioneer in this direction. However, by design PointNet does not capture local structures induced by the metric space points live in, limiting its ability to…

We introduce Patchwork, a new general-purpose shape representation capable of modeling 2D and 3D geometry with a small number of parameters. Patchwork is grounded in a rigorous mathematical framework, providing provable complexity bounds…

This paper introduces a framework designed to accurately predict piecewise linear mappings of arbitrary meshes via a neural network, enabling training and evaluating over heterogeneous collections of meshes that do not share a…

Molecular sciences address a wide range of problems involving molecules of different types and sizes and their complexes. Recently, geometric deep learning, especially Graph Neural Networks, has shown promising performance in molecular…

Despite recent advances in geometric modeling, 3D mesh modeling still involves a considerable amount of manual labor by experts. In this paper, we introduce Mesh Draping: a neural method for transferring existing mesh structure from one…

We propose the use of a Transformer to accurately predict normals from point clouds with noise and density variations. Previous learning-based methods utilize PointNet variants to explicitly extract multi-scale features at different input…

Graph Neural Networks (GNN) can capture the geometric properties of neural representations in EEG data. Here we utilise those to study how reinforcement-based motor learning affects neural activity patterns during motor planning, leveraging…

Neural implicit shape representations are an emerging paradigm that offers many potential benefits over conventional discrete representations, including memory efficiency at a high spatial resolution. Generalizing across shapes with such…

Characterization of quantum objects, being them states, processes, or measurements, complemented by previous knowledge about them is a valuable approach, especially as it leads to routine procedures for real-life components. To this end,…

Surface partial differential equations arise in numerous scientific and engineering applications. Their numerical solution on static and evolving surfaces remains challenging due to geometric complexity and, for evolving geometries, the…

Mesh texture synthesis is a key component in the automatic generation of 3D content. Existing learning-based methods have drawbacks -- either by disregarding the shape manifold during texture generation or by requiring a large number of…

Real-world objects and environments are predominantly composed of edge features, including straight lines and curves. Such edges are crucial elements for various applications, such as CAD modeling, surface meshing, lane mapping, etc.…

Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling…

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid,…

Point cloud learning often rests on the premise that observed samples are noisy traces of an underlying geometric object, such as a manifold embedded in a high-dimensional feature space. Yet much of this geometry is not captured directly by…

Brain surface analysis is essential to neuroscience, however, the complex geometry of the brain cortex hinders computational methods for this task. The difficulty arises from a discrepancy between 3D imaging data, which is represented in…