3D Axial-Attention improves lung nodule classification accuracy.
problem Limited 3D attention in existing methods.
method Proposes 3D Axial-Attention network with 3D positional encoding.
result 3D Axial-Attention achieves state-of-the-art performance.
3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D…
3D convolutional neural networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. In this paper, we present a 3D-CNN based method to learn distinct local geometric features of interest within an object. In this context, the voxelized representation may not be sufficient to captu…
Local-HDP learns independent topics for each 3D object category in real-time.
problem Learning independent topics for each 3D object category in real-time.
method Local-Hierarchical Dirichlet Process (Local-HDP) with online variational inference.
result Local-HDP outperforms other approaches in accuracy, scalability, and memory efficiency.
Study how large-scale flows align small-scale vortices in 3D Euler equations.
problem Understanding how large-scale flows align small-scale vortices in 3D Euler equations.
method Constructing a Lagrangian coordinate to identify when the Lie bracket is zero and investigating the locality of the pressure term.
result Clarified conditions under which small-scale vortices are aligned by large-scale flows.
Study 3d N=1 vacua from M-theory compactification on Spin(7) space.
problem Quantum corrections in 3d N=1 vacua from M-theory compactification.
method Use Higgs bundles to analyze 3d N=1 vacua and track corrections.
result Topological anomalies are robust and calculable in 3d effective field theory.
A diagrammatic language for 3D manifolds with boundary.
problem Representing and manipulating 3D manifolds with boundary.
method Diagrammatic calculus and local moves.
result Completeness of the diagrammatic calculus proved.
3D analog of Whitney's planarity criterion for 2-complexes.
problem Embedding 2-complexes in 3-space.
method Proving dual matroids of 2-complexes are graphic if and only if the complexes embed in 3-space.
result Simply connected and locally 2-dimensional complexes embed in 3-space if and only if their dual matroids are graphic.
We develop three efficient approaches for generating visual explanations from 3D convolutional neural networks (3D-CNNs) for Alzheimer's disease classification. One approach conducts sensitivity analysis on hierarchical 3D image segmentation, and the other two visualize network activations on a spatial map. Visual chec…
Authors classify 3D locally standard T-pseudomanifolds under weaker conditions.
problem Classifying equivariant homeomorphism types of 3D locally standard T-pseudomanifolds.
method Introduced and classified by characteristic data under homotopy equivalence condition.
result Condition for classification can be removed when dimension is at most three.
We consider learning based methods for visual localization that do not require the construction of explicit maps in the form of point clouds or voxels. The goal is to learn an implicit representation of the environment at a higher, more abstract level. We propose to use a generative approach based on Generative Query N…
Graph convolutional neural networks (Graph-CNNs) extend traditional CNNs to handle data that is supported on a graph. Major challenges when working with data on graphs are that the support set (the vertices of the graph) do not typically have a natural ordering, and in general, the topology of the graph is not regular …
Classifies 3D F-manifolds with or without Euler fields.
problem Local classification of 3D F-manifolds.
method Integrability condition on multiplication in holomorphic tangent bundle.
result Local classification of 3D F-manifolds.
A 3D almost-Riemannian manifold is a generalized Riemannian manifold defined locally by 3 vector fields that play the role of an orthonormal frame, but could become collinear on some set $\Zz$ called the singular set. Under the Hormander condition, a 3D almost-Riemannian structure still has a metric space structure, wh…
Paper extends 2D ZSAD to 3D MRI without training, achieving robust anomaly detection.
problem Challenges in extending zero-shot anomaly detection to 3D medical images.
method Constructs localized volumetric tokens by aggregating 2D slices processed by 2D foundation models.
result Training-free, batch-based ZSAD effectively extends from 2D encoders to full 3D MRI volumes.
The paper proposes methods for volumetric parameterization of 3D solid manifolds.
problem Complex structure of solid manifolds makes conventional approaches ineffective.
method Incorporates models to preserve geometric structure, achieve density equalization, and balance distortions.
result Various 3D manifold parameterizations with different properties can be achieved.
The ability to use a 2D map to navigate a complex 3D environment is quite remarkable, and even difficult for many humans. Localization and navigation is also an important problem in domains such as robotics, and has recently become a focus of the deep reinforcement learning community. In this paper we teach a reinforce…
Scientific imaging techniques such as optical and electron microscopy and computed tomography (CT) scanning are used to study the 3D structure of an object through 2D observations. These observations are related to the original 3D object through orthogonal integral projections. For common 3D reconstruction algorithms, …
PointGMM learns hGMMs from point clouds for 3D shape representation.
problem Lack of shape priors and non-local information in point cloud representations.
method Neural network that learns hierarchical Gaussian mixture models (hGMMs) for 3D shapes.
result Generative model learns meaningful latent space for interpolations and novel shape synthesis.
Proves Steiner and tube formulae for 3D contact sub-Riemannian surfaces.
problem Calculating surface properties in complex geometric structures.
method Develops a local Steiner formula for regular surfaces in 3D contact sub-Riemannian manifolds.
result Establishes a formula for surface expansion in arbitrary regions of contact sub-Riemannian manifolds.
We study geometric consistency relations between angles on 3-dimensional (3D) circular quadrilateral lattices -- lattices whose faces are planar quadrilaterals inscribable into a circle. We show that these relations generate canonical transformations of a remarkable ``ultra-local'' Poisson bracket algebra defined on di…
Modeling 3D continua with singular points using Yin sets.
problem Treat singular points as central subjects in 3D continuum topology.
method Model 3D continua as Yin sets, regular open semianalytic sets with bounded boundary.
result Characterize local and global topology of Yin sets.
3D contact manifolds have optimal higher systolic ratios.
problem Optimizing higher systolic ratios in 3D contact manifolds.
method Proving Besse contact forms maximize certain ratios.
result Besse contact forms are local maximizers of higher systolic ratios.
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.
The paper classifies 3D paracontact and almost paracosymplectic spaces.
problem Classifying 3D paracontact and almost paracosymplectic spaces.
method Detailed structure analysis and local classification for all possible values of κ.
result Local classification of paracontact metric and almost paracosymplectic (κ,μ)-spaces for every possible value of κ.
Novel approach combines local and global brain changes for AD prediction.
problem Detecting Alzheimer's disease through local and global brain changes.
method Patch-based 3D-CNNs combined with global topological features for multi-scale brain tissue connectivity.
result Average precision score of 0.95 for classifying cognitively normal subjects and AD patients (prevalence ~55%).
Researchers found 5 local fields to uniquely describe 3D director fields, related through 6 differential relations.
problem Understanding the compatibility conditions for 3D director fields.
method Employed the method of moving frames.
result A director field is fully determined by five local fields related through six differential relations.
A class of 3d N=2 supersymmetric gauge theories are constructed and shown to encode the simplicial geometries in 4-dimensions. The gauge theories are defined by applying the Dimofte-Gaiotto-Gukov construction in 3d/3d correspondence to certain graph complement 3-manifolds. Given a gauge theory in this class…
3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a 3D object, and its rotated clone, will look unrelated to each other after passing through to the last layer of a network. Instead, an idealized model would preserve a meaningful r…
While deep learning in 3D domain has achieved revolutionary performance in many tasks, the robustness of these models has not been sufficiently studied or explored. Regarding the 3D adversarial samples, most existing works focus on manipulation of local points, which may fail to invoke the global geometry properties, l…
New framework segments 3D scenes using neural algorithms and sub-Riemannian geometry.
problem Effective scene segmentation in 3D vision.
method Neurogeometric sub-Riemannian model, harmonic analysis, neural-based stereo correspondence.
result Sub-Riemannian metric is central to effective scene segmentation.
Study investigates induced geometry on surfaces in 3D contact manifolds.
problem Understanding the metric structure on surfaces embedded in 3D contact sub-Riemannian manifolds.
method Defined a coefficient to characterize characteristic points and identified global conditions for finite induced distance.
result Proved induced distance finite for certain surfaces with isolated characteristic points.
Deep convolutional neural networks (CNNs) have shown outstanding performance in the task of semantically segmenting images. However, applying the same methods on 3D data still poses challenges due to the heavy memory requirements and the lack of structured data. Here, we propose LatticeNet, a novel approach for 3D sema…
Study on 3D manifolds with specific tensor structures and their properties.
problem Characterizing 3D Riemannian manifolds with tensor structures.
method Investigation of locally conformal Riemannian product manifolds and their associated structures.
result Conditions for additional structures to be parallel and properties of almost Einstein and Einstein manifolds.
HLTF generates chemically valid 3D molecules with improved topology control.
problem Generating chemically valid 3D molecules is challenging due to bond topology errors.
method HLTF uses a latent multi-scale plan for global context and a constraint-aware sampler to suppress topology-driven failures.
result HLTF achieves high validity and uniqueness on QM9 and GEOM-DRUGS datasets.
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…
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.
Unified Higgs bundle vacua from M-theory on Spin(7) spaces.
problem Unifying Higgs bundle vacua from different string compactifications.
method Developed formalism for M-theory on local Spin(7) spaces and constructed explicit solutions.
result Unified 3D effective field theory from 4D M- and F-theory vacua.
Volumetric analysis of brain ventricle (BV) structure is a key tool in the study of central nervous system development in embryonic mice. High-frequency ultrasound (HFU) is the only non-invasive, real-time modality available for rapid volumetric imaging of embryos in utero. However, manual segmentation of the BV from H…
In this paper a conformal classification of three dimensional left-invariant sub-Riemannian contact structures is carried out; in particular we will prove the following dichotomy: either a structure is locally conformal to the Heisenberg group H3, or its conformal classification coincides with the metric one…
First constructed genus 2 Cantor set in 3D space.
problem Constructing a geometrically self-similar Cantor set of genus 2.
method Geometrically self-similar construction in R3. result First uniformly quasiregular mapping with a genus 2 Cantor set Julia set.
The study characterizes and proves properties of 3D Poisson quasi-Nijenhuis manifolds.
problem Characterizing and understanding 3D Poisson quasi-Nijenhuis manifolds.
method Characterization through deformation and application of Haantjes structures.
result Every 3D Poisson quasi-Nijenhuis manifold is a Haantjes manifold.
Topology-GS improves 3D GS for better structural and feature integrity.
problem Compromised pixel-level and feature-level integrity in 3D GS.
method Incorporates Local Persistent Voronoi Interpolation (LPVI) and PersLoss based on persistent homology.
result Topology-GS outperforms existing methods in PSNR, SSIM, and LPIPS metrics.
Classifies left invariant Kundt structures on 3D Lie groups.
problem Understanding Kundt spacetimes and their properties.
method Analyzes local structure and properties of left invariant Kundt structures.
result Classifies all left invariant Kundt structures on 3D simply connected unimodular Lie groups.
New approach connects 3D Chern-Simons theory to spectral networks.
problem Understanding Chern-Simons invariants in 3D manifolds.
method Constructing equivalences between bundles and spectral networks.
result New formulas for Chern-Simons invariants of 3D manifolds.
Improves local learning models for complex feature extraction.
problem Limited use of simple model families in local learning.
method Uses complex local model families to extract features.
result Demonstrates applications in various fields.
Softens tilings in 3D space, proving conjectures about polyhedral tilings.
problem Proving that all locally polyhedral tilings in 3D space can be softened.
method Developed a new edge-bending algorithm to prove the statement.
result Proved conjectures about polyhedral tilings in 3D space and the plane.
Novel boundary integral equations for Dirac operators in 3D Lipschitz domains.
problem Developing equations for Dirac operators in complex 3D domains.
method First-kind boundary integral equations, generalized Garding inequalities, Fredholm operators, finite dimensional kernels, Betti numbers.
result Finite dimensional kernels equal to the sum of Betti numbers, explaining the bilinear forms.