In this paper, we discuss the global aspect of the geometric dynamics of volumetric expansion and its application to the problem of the existence in the space-time of compact and complete spacelike hypersurface.
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48 results for “volumetric expansion”
Corrected proof for C^2UCB contextual combinatorial bandit's regret bound.
problem Error in proof of C^2UCB contextual combinatorial bandit's regret bound.
method Demonstrated and corrected an error in the proof of volumetric expansion of the moment matrix.
result Proved a relaxed inequality that yields the originally-stated regret bound.
The paper studies the consistency of mean curvature flow via volumetric varifolds.
problem Consistency of mean curvature flow.
method Discretization using volumetric varifolds and derivation of Brakke approximate equality.
result Derivation of a Brakke approximate equality involving varifold masses and approximate mean curvatures.
DVAO predicts volumetric ambient occlusion for real-time volume rendering.
problem Predicting per-voxel ambient occlusion in volumetric data sets.
method Deep learning neural network that considers global information through transfer function.
result DVAO supports real-time volume interaction and generalizes to various modalities.
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.
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other topological spaces---such as a sphere () or a unit ball ()---…
The conformal method is a technique for finding Cauchy data in general relativity solving the Einstein constraint equations, and its parameters include a conformal class, a conformal momentum (as measured by a densitized lapse), and a mean curvature. Although the conformal method is successful in generating constant me…
Bayesian PixelCNN improves semi-supervised learning in MRI data.
problem Lack of robust uncertainty measures in deep generative models for MRI data.
method Extended PixelCNN to volumetric MRI data and reformulated as a deep Gaussian process.
result Improved semi-supervised learning performance in MRI data.
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.
Estimates for -capacities on symmetric manifolds.
problem Estimating relative -capacities on symmetric manifolds.
method Rotationally symmetric manifolds and novel volumetric estimates.
result Sharp weak -embeddings and precise lower bounds of principal -frequencies.
Deep learning improves 3D microscopy resolution without matched target images.
problem Anisotropic resolution in volumetric fluorescence microscopy.
method Cycle-consistent generative adversarial network trained on unpaired 2D images.
result Enhanced axial resolution and restored details between imaging planes.
Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.
problem Determine thermal conductivity and volumetric heat capacity from boundary measurements.
method Uniqueness proof for isotropic and anisotropic media under thermal diffusivity assumption.
result Uniqueness of thermal properties in all dimensions and up to a gauge in two dimensions.
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.
Disease Detection in Weakly Annotated Volumetric Medical Images using a Convolutional LSTM Networkcs.CV
We explore a solution for learning disease signatures from weakly, yet easily obtainable, annotated volumetric medical imaging data by analyzing 3D volumes as a sequence of 2D images. We demonstrate the performance of our solution in the detection of emphysema in lung cancer screening low-dose CT images. Our approach u…
New method beats volumetric barrier for manifold recovery.
problem Reconstructing latent geometry from noisy distances.
method Orthogonal Ring Distance Estimation Routine (ORDER).
result Achieves pointwise distance estimation of order .
A new 2.5D U-net for 3D segmentation reduces memory constraints.
problem Large storage requirements for 3D convolutions in neural networks.
method Transform volumetric data into sequences of 2D images, apply 2D convolutions, and reconstruct.
result Outperforms existing methods in volumetric segmentation tasks.
New dataset tests mental rotation from single images, improving model understanding of 3D scenes.
problem Understanding how a scene looks from a different viewpoint using a single image.
method Created CLEVR-MRT dataset, explored neural architectures for volumetric scene representations.
result Demonstrated the effectiveness of volumetric representations in answering mental rotation questions.
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.
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…
Radiological imaging of the prostate is becoming more popular among researchers and clinicians in searching for diseases, primarily cancer. Scans might be acquired with different equipment or at different times for prognosis monitoring, with patient movement between scans, resulting in multiple datasets that need to be…
The paper proves a new inequality linking mass and volume in 3D space.
problem Relating mass and volume in 3D space with a sharp inequality.
method Using a monotonicity formula for level sets of a 3-harmonic function.
result Sharp lower bound for ADM mass in terms of Euclidean volume of Ω.
In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, Pólya-Szegö and Aleksandrov-Fenchel inequalities for mean-convex Euclidean domains are obtained. For each inequality, the case of equality is char…
Brain cancer can be very fatal, but chances of survival increase through early detection and treatment. Doctors use Magnetic Resonance Imaging (MRI) to detect and locate tumors in the brain, and very carefully analyze scans to segment brain tumors. Manual segmentation is time consuming and tiring for doctors, and it ca…
Estimation of Z-Thickness and XY-Anisotropy of Electron Microscopy Images using Gaussian Processeseess.IV
Method estimates section thickness and XY anisotropy in ssEM images.
problem Accurate 3D reconstructions require precise section thickness and XY anisotropy estimates.
method Non-parametric Bayesian regression of image statistics.
result Method has lower estimation error compared to existing methods.
A novel approach for 3D lung nodule segmentation using adaptive ROI and multi-view residual learning.
problem Inaccurate nodule segmentation due to fixed ROI and redundant structures.
method Two-stage approach: 2D ROI patch-wise investigation with adaptive ROI strategy, followed by 2D and 3D VOI investigation with deep residual U-Net.
result Significantly robust and accurate nodule segmentation compared to previous methods.
Atrial Fibrillation (AF) is a common electro-physiological cardiac disorder that causes changes in the anatomy of the atria. A better characterization of these changes is desirable for the definition of clinical biomarkers, furthermore, thus there is a need for its fully automatic segmentation from clinical images. In …
Generative models of MRI-derived neuroimaging features and associated dataset of 18,000 samplesq-bio.QM
Generative models create synthetic MRI brain scans for research.
problem Lack of large, diverse medical datasets for machine learning.
method Training generative models on 40,000 MRI scans to produce 18,000 synthetic samples.
result Generated samples improve machine learning model accuracy.
Buried landmines and unexploded remnants of war are a constant threat for the population of many countries that have been hit by wars in the past years. The huge amount of human lives lost due to this phenomenon has been a strong motivation for the research community toward the development of safe and robust techniques…
Single linear solve combines surface reconstruction and uncertainty quantification.
problem Reconstructing surfaces from partial point clouds with uncertainty.
method Geometric Gaussian processes for stochastic surface reconstruction.
result Single linear solve for surface reconstruction with probabilistic capabilities.
Rescaling expansiveness proven for k*-expansive vector fields.
problem Proving rescaling expansiveness for k*-expansive vector fields.
method Introducing and exploring singular-expansive flows.
result Rescaling expansiveness established for k*-expansive vector fields.
Paper proves anisotropic Minkowski inequality and related inequalities.
problem Proving anisotropic Minkowski inequality and related inequalities.
method Utilizes a nonlinear potential theoretic approach.
result Sharp anisotropic Minkowski inequality and related inequalities proved.
Paper develops a new model for forecasting ocean currents.
problem Forecasting the Loop Current and its eddies for the Gulf of Mexico.
method Physics-informed Tensor-train ConvLSTM, incorporating prior physical knowledge.
result PITT-ConvLSTM outperforms state-of-the-art methods in volumetric velocity forecasting.
The paper derives expansions for Green's operators and resolvents using Hadamard methods.
problem Analyzing normally hyperbolic operators and their Green's functions.
method Hadamard expansions for powers of Green's operators and resolvents.
result Derives expansions involving Hadamard coefficients for advanced/retarded Green's operators.
This work improves medical image segmentation with limited annotations using contrastive learning.
problem Lack of labeled data for medical image segmentation.
method Contrastive learning framework for semi-supervised segmentation with domain-specific and problem-specific cues.
result Significant improvements in segmentation performance compared to other methods.
Dissertation tackles zero-shot anomaly detection, focusing on consistent anomalies and proposing CoDeGraph framework.
problem Consistent anomalies bias distance-based zero-shot anomaly detection methods.
method Formalized consistent anomalies, identified similarity scaling and neighbor-burnout phenomena, introduced CoDeGraph framework.
result CoDeGraph effectively suppresses consistent anomalies in zero-shot anomaly detection.
We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to , and so that their boundary is a minimal hypersurface. (Here, is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is b…
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 …
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Taylor expansions improve reinforcement learning policies.
problem Improving reinforcement learning policy optimization.
method Taylor expansion policy optimization.
result Taylor expansions enhance performance of distributed algorithms.
Analytic torsion expansions for symmetric and complex homogeneous spaces.
problem Calculating the full asymptotic expansion of analytic torsion for various spaces.
method Explicit calculation and comparison with existing results.
result Explicit full asymptotic expansions for symmetric and complex homogeneous spaces.
Proved cyclotomic expansion for double twist knots' HOMFLY-PT invariants.
problem Proving cyclotomic expansion for colored HOMFLY-PT invariants of double twist knots.
method Cyclotomic expansion formula for double twist knots.
result Confirmed cyclotomic expansion conjecture for SU(N)-invariants.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
Study of hypersurfaces with specific expansion properties.
problem Existence and properties of hypersurfaces with prescribed null expansion.
method Adapted Eichmair's Perron approach for existence.
result Topology theorem for hypersurfaces with prescribed null expansion.
Study evaluates methods for expanding communities in hypergraphs using random walks.
problem Expanding communities in hypergraphs using random walks.
method Clique-expansion and tensor methods evaluated; hybrid method proposed.
result Parameter regimes identified where methods outperform each other.
AI tool automates blood segmentation from head CT scans after SAH.
problem Accurate volumetric assessment of SAH patients for clinical and prognostic implications.
method Transformer-based Swin UNETR architecture for noncontrast CT scans.
result High accuracy and robust performance across internal and external validation cohorts.
The paper predicts brain tumor patient survival using segmentation and features.
problem Predicting overall survival of brain tumor patients.
method Automated brain tumor segmentation and use of age, shape, and volumetric features for prediction.
result Random forest classifier achieves 59% accuracy on test dataset and 67% on gross total resection dataset.
Asymmetric expansion preserves convexity in hyperbolic geometry.
problem Maintaining convexity in hyperbolic geometry under asymmetric expansions.
method Generalizing earlier results on radial expansion to asymmetric expansion.
result Asymmetric expansion of hyperbolic convex sets remains convex.
In microsurgery, lasers have emerged as precise tools for bone ablation. A challenge is automatic control of laser bone ablation with 4D optical coherence tomography (OCT). OCT as high resolution imaging modality provides volumetric images of tissue and foresees information of bone position and orientation (pose) as we…