We solve 6-DoF localisation and 3D reconstruction using deep state-space models.
problem 6-DoF localisation and dense 3D reconstruction in spatial environments.
method Approximate Bayesian inference in a deep state-space model combining learning and domain knowledge.
result Near state-of-the-art performance on UAV flight data.
One of the key challenges of visual perception is to extract abstract models of 3D objects and object categories from visual measurements, which are affected by complex nuisance factors such as viewpoint, occlusion, motion, and deformations. Starting from the recent idea of viewpoint factorization, we propose a new app…
In this paper, we prove (1): for any closed contact three-manifold with a C∞-generic contact form, the union of periodic Reeb orbits is dense, (2): for any closed surface with a C∞-generic Riemannian metric, the union of closed geodesics is dense. The key observation is C∞-closing lemma for 3D R…
Defines a map connecting 3d-index and skein module.
problem Connecting mathematical physics predictions with topological quantum field theory.
method Defines a map from skein module to Laurent series ring.
result The map fulfills a supersymmetry prediction and is part of a conjectural topological quantum field theory.
Classifies manifolds with dense conjugacy classes in their mapping class groups.
problem Classifying manifolds based on conjugacy classes in their mapping class groups.
method Analyzing connected orientable 2-manifolds and their mapping class groups.
result Mapping class groups of certain manifolds have dense conjugacy classes.
Study sub-Riemannian geodesics on a Heisenberg 3D nil-manifold.
problem Characterize geodesics on a specific nil-manifold.
method Analyze the projection of sub-Riemannian structure, describe geodesic flow dynamics, and estimate sub-Riemannian geodesics.
result Sharp bounds and estimates for sub-Riemannian geodesics.
The article explains Rao distances and conformal mappings for 3D objects.
problem Calculating distances and preserving angles in 3D objects.
method Proposed constructions of distances and angle-preserving mappings.
result Application to virtual tourism and line integrals in complex planes.
Propose a new 3d quantum trace map that agrees with Garoufalidis and Yu's construction and extends to certain manifolds with ideal triangulated boundaries.
problem Relationship between two constructions of 3d quantum trace maps.
method Propose a new 3d quantum trace map.
result Proposed 3d quantum trace map agrees with Garoufalidis and Yu's construction and extends to certain manifolds with ideal triangulated boundaries.
Non-compact manifolds prevent C0-stable mappings from being dense.
problem Density of C0-stable mappings on non-compact manifolds. method Using topologically critical points to show non-density.
result The set of C0-stable mappings is never dense on non-compact manifolds. Paper connects 3D gravity averages to 2D CFT correlators.
problem Understanding 3D gravity partition functions.
method 3D topological field theories and mapping class group averages.
result Established a correspondence between 3D gravity averages and 2D CFT correlators.
The paper classifies dense conjugacy classes in mapping class groups of locally finite graphs.
problem Identifying which mapping class groups have dense conjugacy classes.
method Developed flux homomorphisms and combinatorial criteria for stability.
result A complete classification for self-similar locally finite graphs and a criterion for stability.
The paper uses facial keypoints to estimate post-surgical pain intensity.
problem Accurately assessing pain levels from self-reported ratings is challenging.
method The approach analyzes 2D and 3D facial keypoints to estimate pain intensity.
result The pain estimation model uses multiple instance learning.
Proves unique maps from certain spaces to others.
problem Uniqueness of equivariant harmonic maps into specific spaces.
method Analyzes maps into irreducible symmetric spaces and Euclidean buildings.
result Proves uniqueness of maps for certain actions.
3D object recognition accuracy can be improved by learning the multi-scale spatial features from 3D spatial geometric representations of objects such as point clouds, 3D models, surfaces, and RGB-D data. Current deep learning approaches learn such features either using structured data representations (voxel grids and o…
3D quantum trace map connects 3-manifold quantizations.
problem Quantization of 3-manifold character varieties.
method Study of stated skein modules and face suspensions.
result Existence of 3D quantum trace map proved.
New proof shows almost all surface group actions are dense.
problem Transitivity of normal subgroups on character varieties.
method Proved almost minimal action of non-trivial normal subgroups.
result Almost all points in character variety have dense orbits.
Study mapping class groups of specific 3D shapes.
problem Computing mapping class groups of certain 3D manifolds.
method Analyzes simply-connected closed smooth manifolds with specific homology properties.
result Computes the mapping class group for given dimensions.
The automatic segmentation of human knee cartilage from 3D MR images is a useful yet challenging task due to the thin sheet structure of the cartilage with diffuse boundaries and inhomogeneous intensities. In this paper, we present an iterative multi-class learning method to segment the femoral, tibial and patellar car…
3D adversarial logos can fool object detectors in real-world settings.
problem Creating robust adversarial attacks in 3D rendering views.
method Constructing 3D adversarial logos via texture mapping and differentiable rendering.
result 3D adversarial logos are more versatile and robust than traditional adversarial patches.
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.
Quantitative susceptibility mapping (QSM) is a powerful MRI technique that has shown great potential in quantifying tissue susceptibility in numerous neurological disorders. However, the intrinsic ill-posed dipole inversion problem greatly affects the accuracy of the susceptibility map. We propose QSMGAN: a 3D deep con…
We show that smooth maps are C1-dense among C1 volume preserving maps.
A method improves Cryo-EM 3D map refinement by regularizing rotation estimation.
problem Noise-robustness vs. data-consistency in Cryo-EM 3D map reconstruction.
method Ellipsoidal support lifting (ESL) for regularizing and approximating the global minimizer over Riemannian manifolds.
result The induced bias due to regularizing effect of ESL estimates better rotations than global optimisation.
Maximal representations in symplectic lattices proven for most cases.
problem Understanding maximal representations in symplectic lattices.
method Analyzing mapping class group orbits and continuous deformations of maximal diagonal representations.
result Proof of maximal representations in most lattices of Sp(2n,R).
Integral points are potentially dense in character varieties of quasi-projective varieties.
problem Density of integral points in character varieties of quasi-projective varieties.
method Reduction to Riemann surfaces and use of Corlette-Simpson work.
result Integral points have Zariski-dense orbit under the mapping class group.
3D dust map of the Milky Way improves resolution and accuracy.
problem Reconstructing the 3D dust distribution in the Milky Way.
method Gaussian process regression on spherical coordinates with iterative grid refinement.
result Improved 3D dust map with increased resolution and accuracy.
Autonomous driving requires 3D perception of vehicles and other objects in the in environment. Much of the current methods support 2D vehicle detection. This paper proposes a flexible pipeline to adopt any 2D detection network and fuse it with a 3D point cloud to generate 3D information with minimum changes of the 2D d…
Study of conjugacy classes in infinite-type surfaces' mapping class groups.
problem Characterizing conjugacy classes in infinite-type surfaces' mapping class groups.
method Model-theoretic methods developed by Kechris, Rosendal, and Truss.
result Detailed classification of conjugacy classes in mapping class groups of infinite-type surfaces.
One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N=2 SCFT T[M3] --- or, rather, a "collection of SCFTs" as we refer to it in the paper --- for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgerie…
The paper studies decay near singularities of 3d Yang-Mills-Higgs fields.
problem Understanding isolated singularities of 3d Yang-Mills-Higgs fields.
method Derives decay estimates and applies removable singularity theorems.
result Generalizes removable singularity theorems for 3d Yang-Mills-Higgs fields.
The paper explores the twisted Rokhlin property in mapping class groups of surfaces.
problem Classifying surfaces whose mapping class groups have the twisted Rokhlin property.
method Generalizing the Rokhlin property to the twisted version, the authors classify surfaces based on their mapping class groups' properties.
result The mapping class groups of connected orientable infinite-type surfaces without boundaries have the twisted Rokhlin property, while those of other surfaces do not.
Improved 3D ECG feature attributions for clinical interpretation.
problem Lack of interpretability in deep learning models for 12-lead ECG analysis.
method Cross-modal mapping of feature attributions from 12-lead ECG models onto CineECG 3D space.
result Mapped feature attributions yield higher Dice scores than standard 12-lead attributions.
Agent learns to navigate uncertain 3D maps using a hybrid planner.
problem Planning in 3D environments with uncertain topological maps.
method Hierarchical strategy combining graph planner and local policy, data-driven learning with neural network.
result Machine learning can overcome missing information in probabilistic topological maps.
Let M be a complete metric ANR-space such that for any metric compactum K the function space C(K,M) contains a dense set of Bing (resp., Krasinkiewicz) maps. It is shown that M has the following property: If f:X→Y is a perfect surjection between metric spaces, then C(X,M) with the source limitati…
The paper shows dense and residual sets of continuous maps with positive metric mean dimension.
problem Understanding the genericity of continuous maps with positive metric mean dimension.
method Analyzing continuous maps on compact Riemannian manifolds and Cantor sets.
result The set of continuous maps with metric mean dimension equal to a given value is dense and, for the dimension, residual in the space of continuous maps.
The tangential map is a map on the set of smooth planar curves. It satisfies the 3D-consistency property and is closely related to some well-known integrable equations.
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 ConvNets improved with Project & Excite for medical imaging segmentation.
problem Improving segmentation performance in 3D medical imaging.
method Proposed Project & Excite (PE) modules for 3D F-CNNs, extending 2D recalibration methods.
result Project & Excite modules boost segmentation performance up to 0.3 in Dice Score.
Maximal cusps are not dense on Teichmüller space for infinite-type surfaces.
problem Characterizing dense points in the Bers boundary of Teichmüller space for infinite-type surfaces.
method Quasiconformal deformations and analytic conditions.
result Maximal cusps cannot approach certain points on the Bers boundary.
We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equivariant convolutions to map between such representations. These SE(3)-equivariant convolutions utilize kernels which are parameterized as a …
Algorithm aligns 3D density maps using Wasserstein distance.
problem Aligning 3D density maps in cryogenic electron microscopy.
method Minimizing 1-Wasserstein distance after rigid transformation using Bayesian optimization.
result Improved accuracy and efficiency in protein molecule alignment.
Symmetrizes 4d and 3d BPS quivers for Argyres-Douglas theories.
problem Understanding the relationship between 4d and 3d BPS quivers.
method Analyzes geometric backgrounds and uses skein modules to derive quiver partition functions.
result Proves isomorphism between 4d wall-crossing and unlinking of symmetric quivers.
The period map for 4-manifolds is dense and surjective under certain conditions.
problem Understanding the space of metrics on 4-manifolds and their harmonic forms.
method Constructing families of metrics by stretching along hypersurfaces.
result The period map is dense and surjective for 4-manifolds with b+=1. 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…
New family of measurable pseudo-Anosov maps on spheres.
problem Generalizing pseudo-Anosov maps to measurable ones.
method Continuous family of homeomorphisms on sphere, semi-conjugate to core tent map.
result Measurable pseudo-Anosov maps have invariant dense streamlines with uniform measures.
When using Convolutional Neural Networks (CNNs) for segmentation of organs and lesions in medical images, the conventional approach is to work with inputs and outputs either as single slice (2D) or whole volumes (3D). One common alternative, in this study denoted as pseudo-3D, is to use a stack of adjacent slices as in…
Study mapping class group action on character varieties, proving Kronecker's Theorem.
problem Topological-dynamical action of mapping class group on character varieties.
method Analyzes Tn-character variety and dense orbit conditions. result Provides a dynamical proof of Kronecker's Theorem.
We construct a smooth compact n-dimensional manifold Y with one point singularity such that all its Lipschitz homotopy groups are trivial, but Lipschitz mappings Lip(S^n,Y) are not dense in the Sobolev space W^{1,n}(S^n,Y). On the other hand we show that if a metric space Y is Lipschitz (n-1)-connected, then Lipschitz …