PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
problem Efficiently modeling 3D geometry for computer graphics, robotics, and games.
method Transformer-based autoregressive model for predicting mesh vertices and faces.
result PolyGen produces high-quality, usable 3D meshes and competitive conditional performance.
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…
Differentiable voxelization for 3D meshes with GPU acceleration.
problem Efficient and accurate voxelization of 3D meshes.
method Differentiable voxelization using winding number and solid angles, with GPU acceleration and neural network deformation.
result State-of-the-art performance in accuracy and efficiency on the ShapeNet dataset.
A neural atlas simplifies 3D geometry simulation by avoiding meshing.
problem Simulation of complex 3D geometries with thin features or non-trivial topology.
method Learned geometric representation of overlapping volumetric coordinate charts, trained from point-cloud or level-set data.
result The learned atlas enables different solvers without re-meshing or re-parametrization.
Generative model disentangles 3D shapes into independent factors.
problem Learning rich representations of deformable 3D shapes.
method Supervised 3D mesh-convolutional Variational AutoEncoder with latent feature disentanglement.
result Explicit disentanglement of latent factors improves shape generation and downstream tasks.
Parallel algorithm for conformal parameterization of 3D surfaces.
problem Computational difficulties with high-resolution 3D surface meshes.
method Partitioning surfaces into subdomains, parallel local parameterization, partial welding for boundary integration, solving Laplace equation.
result Significant improvement in computational time and accuracy compared to existing methods.
Unsupervised mesh disentanglement separates identity and pose.
problem Geometric disentanglement for 3D deformable models.
method CFAN-VAE architecture using conformal factor and normal features.
result CFAN-VAE achieves state-of-the-art performance on unsupervised geometric disentanglement.
LION generates high-quality 3D shapes using hierarchical latent diffusion models.
problem Creating high-quality 3D shapes for digital artists.
method Hierarchical Latent Point Diffusion Model (LION) with a global shape latent and point-structured latent space.
result LION achieves state-of-the-art generation performance on ShapeNet benchmarks.
Highly expressive models such as deep neural networks (DNNs) have been widely applied to various applications. However, recent studies show that DNNs are vulnerable to adversarial examples, which are carefully crafted inputs aiming to mislead the predictions. Currently, the majority of these studies have focused on per…
Instantiation-Net reconstructs 3D mesh from single 2D image for right ventricle.
problem Reconstructing 3D shape from limited 2D images for surgical navigation.
method Combines DCNN for feature extraction and GCN for mesh reconstruction.
result Demonstrates practical strength and potential clinical use.
EuLearn creates diverse 3D topological datasets for machine learning.
problem Training machine learning systems to discern topological features.
method Developed novel sampling and neural network architectures for graph and manifold data.
result Incorporating topological information improves deep learning performance on EuLearn datasets.
Worldsheet wraps a 3D mesh sheet onto a single image to synthesize novel views.
problem Synthesizing novel views from a single image with large viewpoint changes.
method Shrink-wrapping a planar mesh sheet onto the input image, consistent with learned depth.
result Worldsheet consistently outperforms prior methods on single-image view synthesis.
Point cloud is the most fundamental representation of 3D geometric objects. Analyzing and processing point cloud surfaces is important in computer graphics and computer vision. However, most of the existing algorithms for surface analysis require connectivity information. Therefore, it is desirable to develop a mesh st…
Paper presents a consistent discretization for Hodge decomposition on volumetric meshes.
problem Discretization of Hodge decomposition for vector fields on volumetric meshes.
method Edge-based Nedelec elements and face-based Crouzeix-Raviart elements interplay.
result Stable and efficient method for large-sized models with good performance.
AQFC method estimates mesh curvatures using quadratic surfaces.
problem Estimating curvatures for irregular polygonal meshes.
method Local approximation of vertices and normals by quadratic surfaces, computed as implicit surfaces.
result AQFC provides robust curvature estimation for irregular meshes.
PointTriNet generates 3D triangulations from point clouds efficiently and scalably.
problem Generating a triangulation among a set of points in 3D space.
method Iteratively applies a classification network and a proposal network over nearby points and triangles, using a novel triangle-relative input encoding.
result Generates robust and scalable triangulations for 3D learning pipelines.
3D dataset for intracranial aneurysms aids deep learning applications.
problem Lack of 3D medical datasets for deep learning.
method Developed an open-access 3D dataset, IntrA, for intracranial aneurysms.
result Demonstrated the challenges and performance of 3D medical datasets.
Two algorithms create high-quality triangular meshes for surfaces with guaranteed angles.
problem Creating high-quality triangular meshes for surfaces with controlled angles.
method MidNormal and GradNormal algorithms generate meshes with specified angle constraints.
result Meshes converge to surfaces as mesh size decreases, maintaining specified angles.
The paper proves a new discrete Laplacian for 3D meshes and shows its superiority over primal construction.
problem Developing a more accurate discrete Laplacian for 3D meshes.
method Proves the Euler-Lagrange equation for the Dirichlet energy using the associated discrete Laplacian of the dual construction.
result The associated discrete Laplacian is optimal in R3 compared to the primal construction. Approximates smooth surfaces using Laguerre geometry meshes.
problem Approximating smooth surfaces in Laguerre geometry.
method Using Laguerre meshes composed of quadrilaterals, cones, and spherical faces.
result Laguerre conjugate nets and directions for surface approximation.
We study data-driven representations for three-dimensional triangle meshes, which are one of the prevalent objects used to represent 3D geometry. Recent works have developed models that exploit the intrinsic geometry of manifolds and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants, which learn…
In this paper, a new algorithm based on differential geometry viewpoint to solve the 3D rotating Navier-Stokes equations with complex Boundary is proposed, which is called Bi-parallel algorithm. For xample, it can be applied to passage flow between two blades in impeller and circulation flow through aircrafts with comp…
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
problem Computing uniformizations for surfaces of genus >1.
method Discrete conformality and uniformization on triangle meshes.
result Discrete uniformizations approximate continuous uniformization for closed surfaces of genus ≥1.
Approximates surfaces using Laguerre geometry with spherical faces.
problem Approximating smooth surfaces using Laguerre geometry.
method Using Laguerre conjugate nets and spherical faces to approximate surfaces.
result Laguerre conjugate nets provide a method for surface approximation.
A CNN on semi-regular meshes classifies brain diseases from MRI scans.
problem Classifying brain diseases from MRI scans.
method Developed a vertex-based graph CNN for semi-regular triangulated meshes.
result Vertex-based graph CNN outperformed spectral graph CNN in classifying MCI and AD.
The reconstruction of an object's shape or surface from a set of 3D points plays an important role in medical image analysis, e.g. in anatomy reconstruction from tomographic measurements or in the process of aligning intra-operative navigation and preoperative planning data. In such scenarios, one usually has to deal w…
Paper studies superconvergence on surface meshes using gradient recovery.
problem Proving superconvergence on deviated surfaces.
method Introduces geometric supercloseness and an algorithmic framework for gradient recovery.
result Validates theoretical results with numerical examples.
Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenien…
Paper generalizes discrete uniformization for genus-zero surfaces.
problem Discrete uniformization for surfaces of genus zero.
method Reduction to planar cases via stereographic projections.
result Generalization of discrete uniformization to genus-zero surfaces.
Unified framework designs LK structures using integer twists on non-manifold meshes.
problem Binary twisting limits topological possibilities and structural behaviors.
method Generalizes twist formulation to arbitrary integer labels for non-manifold meshes.
result Integer twists enable full connectivity and dynamic folding/articulation.
Generative model creates high-quality meshes from point clouds.
problem Creating accurate meshes from point cloud data.
method Modeling point cloud generation as sphere deformation through deep neural networks.
result The model efficiently generates high-quality meshes from point clouds.
In this paper we are interested in defining affine structures on discrete quadrangular surfaces of the affine three-space. We introduce, in a constructive way, two classes of such surfaces, called respectively indefinite and definite surfaces. The underlying meshes for indefinite surfaces are asymptotic nets satisfying…
A new method monitors unstructured 3D shapes without registration.
problem Error-prone registration and mesh reconstruction steps in PCD monitoring.
method Intrinsic geometric properties of shapes, using Laplacian and geodesic distances.
result Effective monitoring of defects without registration and mesh reconstruction.
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…
Study characterizes bladder motion using dynamic MRI and statistical analysis.
problem Limited volume coverage in dynamic MRI sequences hinders 3D shape reconstruction.
method 3D dense velocity measurements, LDDMM framework, statistical characterization, mean curvature changes, surface deformation analysis.
result Stable shape descriptor for characterizing bladder surface dynamics.
We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean curvature integrand locally. We show that this class is Möbius invariant. Isoth…
New method for surface analysis using restricted deformation bases.
problem Surface registration and comparison without pre-registered data.
method Elastic Riemannian metrics with basis-restricted transformations.
result Effective implementation on human body and face scans.
STM maps improve terrain perception for autonomous robots.
problem Perception of terrain for autonomous robots in general environments.
method Stochastic triangular mesh (STM) technique for 2.5-D surface mapping.
result STM maps are more accurate than standard elevation maps.
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
New method avoids surface self-collision in geometric optimization.
problem Avoiding self-collision in surface optimization.
method Developed a numerical framework using tangent-point energy and fractional Sobolev inner product.
result Successfully accelerated collision avoidance scheme for triangle meshes.
Optimally estimate distances on surfaces using reconstructed meshes.
problem Estimating intrinsic distances on smooth submanifolds.
method Reconstruction of the surface using a tangential Delaunay complex, and Isomap variant.
result Minimax optimality achieved for distance estimation.
Pix2Shape learns 3D scene representations from single images without supervision.
problem Learning 3D scene information from a single image without supervision.
method Pix2Shape uses an encoder, decoder, and critic network to generate 2.5D surfel-based reconstructions.
result Pix2Shape can generate complex 3D scenes from a single image, scaling with on-screen resolution.
Develops a method for conformal parameterization of point clouds without fixed boundaries.
problem Desirable distortion in fixed-boundary parameterizations of point clouds.
method Free-boundary conformal parameterization method involving approximation of point cloud Laplacian and boundary treatment.
result High-quality point cloud meshing achieved through the proposed method.
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional latent scenes, due to challenges in both modeling and inference. Accounting for th…
Proposes polynomial neural networks for improved function approximation in various tasks.
problem Improving function approximation in various tasks like image generation, face verification, and 3D mesh representation learning.
method Introduces polynomial neural networks (Π-Nets) and three tensor decompositions to reduce parameter count and enhance expressiveness. result Demonstrates that Π-Nets can produce state-of-the-art results in challenging tasks without non-linear activation functions. A pair of pants is a genus zero orientable surface with three boundary components. A pants decomposition of a surface is a finite collection of unordered pairwise disjoint simple closed curves embedded in the surface that decompose the surface into pants. In this paper we present two Morse theory based algorithms for p…
Study on 3D surfaces and tangles formed by Poncelet triangles.
problem Geometric and topological properties of 3D surfaces and tangles.
method Exploration of Poncelet triangles and associated points.
result Properties of 3D surfaces and tangles formed by Poncelet triangles.
Extends SW and GSW to compare heterogeneous joint distributions.
problem Limited applicability of SW and GSW to heterogeneous joint distributions.
method Introduces HHRT and PGRT to extend SW and GSW.
result H2SW distance for heterogeneous joint distributions.