Proposes a multi-level learning approach for 3D object recognition.
problem Improving 3D object recognition accuracy through multi-scale spatial features.
method End-to-end multi-level learning on a multi-level voxel grid.
result Comparable object recognition performance with lower memory usage.
When working with three-dimensional data, choice of representation is key. We explore voxel-based models, and present evidence for the viability of voxellated representations in applications including shape modeling and object classification. Our key contributions are methods for training voxel-based variational autoen…
Paper presents voxel graph operators for vector data models.
problem Efficient conversion and analysis of geometric models.
method Topological voxelization, graph construction, differential operator derivation.
result Discrete differential and integral operators from voxel complexes.
Diffusion MRI (dMRI) provides the ability to reconstruct neuronal fibers in the brain, in vivo, by measuring water diffusion along angular gradient directions in q-space. High angular resolution diffusion imaging (HARDI) can produce better estimates of fiber orientation than the popularly used diffusion tens…
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…
Partial soft-matching distance improves neural representation comparison by allowing some neurons to remain unmatched.
problem Neural representations are noisy and contain outliers, making traditional matching methods unreliable.
method Extends soft-matching distance to a partial optimal transport setting, allowing some neurons to remain unmatched.
result Partial soft-matching provides robust correspondences that are more reliable under noise and outliers.
3D neural network models atomistic potentials in complex alloys.
problem Designing robust atomistic potentials for complex alloys is computationally expensive and time-consuming.
method Voxelized atomic configurations and 3D convolutional neural networks to learn atomic interactions.
result 3D convolutional neural networks effectively model atomistic potentials in complex alloys.
Geometric vector perceptrons improve protein structure learning.
problem Learning from protein structure with efficient and natural representations.
method Introducing geometric vector perceptrons to extend dense layers for Euclidean vectors, integrating geometric and relational reasoning.
result Improves model quality assessment and computational protein design over existing methods.
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.
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…
A two-stage CNN approach for brain tumor segmentation.
problem Brain tumor segmentation with class imbalance.
method Cascade V-Net architecture with ROI masks.
result Improved brain tumor segmentation accuracy.
Generic Hitchin representations generate dense subgroups.
problem Understanding dense subgroups in SL_n(R) representations.
method Using a theorem by Rapinchuk, Benyash-Krivetz, and Chernousov.
result Generic Hitchin representations are strongly dense.
A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of inform…
Voxel-FPN detects 3D objects from point clouds using raw LIDAR data.
problem 3D object detection in point cloud data for autonomous driving.
method Bottom-up voxel extraction and top-down feature fusion.
result Voxel-FPN outperforms baselines on the KITTI-3D benchmark.
New representations of hyperbolic 3-manifold groups into larger groups.
problem Finding representations of hyperbolic 3-manifold groups into larger matrix groups.
method Holonomy representations from projective deformations of hyperbolic structures.
result First examples of strongly dense representations into SL(4,R) and SU(3,1). Deep learning estimates dose voxel kernels from CT data for personalized dosimetry.
problem Accurate estimation of absorbed dose in personalized radionuclide therapy.
method Combining deep learning with CT data to approximate dose voxel kernels from density kernels.
result Deep learning achieved an intersection-over-union score of 0.86 and mean squared error of 1.24×10−4 on real patient data.
The paper studies volume classes and Borel classes for dense group representations.
problem Understanding volume and Borel classes for dense representations of discrete groups.
method Utilizes tools from Kleinian groups and properties of hyperbolic manifolds.
result Volume classes are linearly independent and have additional properties.
DeepFDR uses deep learning for better FDR control in neuroimaging data.
problem Spatial dependence among voxel-based tests in neuroimaging data.
method DeepFDR leverages unsupervised deep learning-based image segmentation.
result DeepFDR outperforms existing methods in FDR control and computational efficiency.
In this paper, we consider voxel selection for functional Magnetic Resonance Imaging (fMRI) brain data with the aim of finding a more complete set of probably correlated discriminative voxels, thus improving interpretation of the discovered potential biomarkers. The main difficulty in doing this is an extremely high di…
The paper finds dense subgroups in certain Lie groups.
problem Finding dense subgroups in Lie groups.
method Constructing dense surface subgroups in specific Lie groups.
result Uniform lattices contain infinitely many dense Hitchin representations.
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).
Deforms surface groups to be Zariski dense in SL(n,R)
problem Finding Zariski dense surface groups in SL(n,R)
method Deforming K-integral representations of surface groups result Generalizes Long and Thistlethwaite's method to SL(n,R)
Proposes a multi-resolution model for prostate cancer classification using mpMRI.
problem Improving voxel-wise classification of prostate cancer using multi-parametric MRI data.
method Multi-resolution Super Learner framework combining local base learners at multiple resolutions and spatial Gaussian kernel smoothing.
result Enhanced voxel-wise classification of prostate cancer status and clinical significance.
DenseHMM improves HMMs by learning dense representations that enable gradient-based optimization.
problem Learning dense representations for hidden states and observables in HMMs.
method DenseHMM uses kernelized transition probabilities and two optimization schemes.
result DenseHMM achieves superior performance and expressiveness compared to standard HMMs.
Multivariate Pattern (MVP) classification holds enormous potential for decoding visual stimuli in the human brain by employing task-based fMRI data sets. There is a wide range of challenges in the MVP techniques, i.e. decreasing noise and sparsity, defining effective regions of interest (ROIs), visualizing results, and…
Cataclysm deformations study Anosov representations and their convergence.
problem Understanding convergence of Anosov representations under deformation.
method Cataclysm deformation of Anosov representations using twisted transverse cocycles.
result Uniform convergence of cataclysm deformations on compact sets.
Cataclysm deformations study Anosov representations, leading to new formulas and non-open sets.
problem Understanding Anosov representations and their deformations.
method Cataclysm deformations based on twisted transverse cocycles.
result Uniform convergence of cataclysm deformations on compact sets.
In many human brain network studies, we do not have sufficient number (n) of images relative to the number (p) of voxels due to the prohibitively expensive cost of scanning enough subjects. Thus, brain network models usually suffer the small-n large-p problem. Such a problem is often remedied by sparse network models, …
fMRI analysis classifies autobiographical memory valence across individuals.
problem Classifying valence of autobiographical memories across different participants.
method Feature selection (ReliefF) combined with boosting methods applied to voxel space data.
result Classification accuracy of 62% in cross-participant setting, significantly higher than previous results.
Sparse representations improve network robustness and stability.
problem The benefits of sparse representations in artificial networks.
method Analysis of sparse networks with sparse weights and activations, simulations on MNIST and Google Speech Command Dataset.
result Sparse networks show significantly improved robustness and stability compared to dense networks.
ViCE uses superpixels to enhance self-supervised learning for better dense visual embeddings.
problem Lack of high-resolution feature maps from self-supervised models.
method Superpixels for dense representation learning, contrasting over regions.
result Improves unsupervised semantic segmentation on benchmarks like Cityscapes and COCO.
New domains of discontinuity found for Anosov representations.
problem Understanding Anosov representations acting on homogeneous spaces.
method Constructing open domains of discontinuity for Anosov representations acting on specific homogeneous spaces.
result Describes the largest possible open domains of discontinuity for Zariski dense Anosov representations.
Odd-dimensional SL(n,Q) contains dense surface subgroups.
problem Finding dense subgroups in SL(n,Q) for odd n.
method Constructing a continuous path of representations.
result Existence of dense surface subgroups in SL(n,Q) for odd n.
Tab2vox converts tabular data into 3D images for improved demand forecasting.
problem Forecasting demand influenced by multi-level causes and large volatility.
method Tab2vox neural architecture search (NAS) model to convert tabular data into 3D voxel images for 3D CNN forecasting.
result 3D CNN forecasting model outperforms existing tabular data techniques.
Generic Hitchin representations avoid hyperplanes in Lie algebras.
problem Properties of Hitchin representations in Lie algebras.
method Defined J(ρ) and used hyperplanes in Lie algebras to show J(ρ)∩H=∅. result Generic G-Hitchin representations avoid hyperplanes in the Lie algebra of G. A novel topological method analyzes fMRI data over time.
problem Analyzing time-varying fMRI data due to noise and person-to-person variation.
method Encoding each time point as a persistence diagram of topological features.
result Time-varying persistence diagrams can cluster participants and study brain state trajectories.
The paper explores mapping class group quotients by Dehn twists and their representations.
problem Finite quotients and representations of mapping class groups by powers of Dehn twists.
method Construction of finite quotients using representations with Zariski dense images into semisimple Lie groups, and Long and Moody's method.
result The Fibonacci TQFT representation is a specialization of the Jones representation in genus 2.
We prove that a dense subgroup of Homeo+(I) is not elementary amenable. We also show that the topological group Homeo+(I) does not satisfy the Stability of the Generators Property, moreover, any finitely generated subgroup of Homeo+(I) admits a faithful discrete representation …
Improved fMRI activation detection for single-subject studies.
problem Challenges in detecting activation in low-signal fMRI studies.
method Model-based approach using MixfMRI R package.
result Reliable activation detection in single-subject fMRI studies.
We propose a globally convergent alternating minimization (AM) algorithm for image reconstruction in transmission tomography, which extends automatic relevance determination (ARD) to Poisson noise models with Beer's law. The algorithm promotes solutions that are sparse in the pixel/voxel-differences domain by introduci…
The success of various applications including robotics, digital content creation, and visualization demand a structured and abstract representation of the 3D world from limited sensor data. Inspired by the nature of human perception of 3D shapes as a collection of simple parts, we explore such an abstract shape represe…
Study shows how to detect representation extendability using conformal measures.
problem Detecting extendability of representations using conformal measures.
method Using higher rank conformal measures and self-joinings of groups.
result Affirmative answer to detect extendability of representations.
Inverse inference, or "brain reading", is a recent paradigm for analyzing functional magnetic resonance imaging (fMRI) data, based on pattern recognition and statistical learning. By predicting some cognitive variables related to brain activation maps, this approach aims at decoding brain activity. Inverse inference ta…
New MRI method maps tissue parameters more accurately by ignoring voxel independence.
problem Voxel independence assumption limits model fitting reliability and repeatability.
method Self-supervised deep variational approach with Gaussian mixture prior.
result Our method outperforms current techniques in dMRI simulations and real data.
MRI method predicts glioma features, survival, and endothelial proliferation.
problem Invasive biopsy limits detection of glioma features due to tumor heterogeneity.
method Voxel-wise, multiparametric MRI radiomics with k-NN classifier.
result Model accurately predicts disease compositions, survival, and endothelial proliferation.
Maximal representations in infinite dimensional Hermitian spaces are studied with boundary maps.
problem Characterizing maximal representations in infinite dimensional Hermitian symmetric spaces.
method Definition of Toledo number, study of boundary maps, geometric constructions.
result Existence and non-existence conditions for maximal representations.
InSphereNet uses infilling spheres for 3D object classification, improving accuracy with fewer parameters.
problem 3D object classification using points, voxels, or images.
method Constructs infilling spheres from signed distance field (SDF) for classification.
result InSphereNet achieves superior accuracy with fewer inputs and parameters.
Generative model learns from designs to create new shapes.
problem Designing new shapes for conceptual optimization.
method Variational autoencoder-decoder architecture for 3D shape synthesis.
result Generator maps latent space to smooth 3D surfaces for optimization.