arXiv research

The paper proposes methods for volumetric parameterization of 3D solid manifolds.

The paper studies the consistency of mean curvature flow via volumetric varifolds.

DVAO predicts volumetric ambient occlusion for real-time volume rendering.

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 …

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.

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 ($\mathbb{S}^2$) or a unit ball ($\mathbb{B}^3$)---…

Deep generative models are rapidly gaining traction in medical imaging. Nonetheless, most generative architectures struggle to capture the underlying probability distributions of volumetric data, exhibit convergence problems, and offer no robust indices of model uncertainty. By comparison, the autoregressive generative…

Paper extends 2D ZSAD to 3D MRI without training, achieving robust anomaly detection.

Estimates for $p$-capacities on symmetric manifolds.

Deep learning improves 3D microscopy resolution without matched target images.

Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and therefore, end-to-end training is limited by GPU memory and data size. To overcome this issue, we introduce a netwo…

Study on uniquely determining thermal properties from boundary temperature and heat flux measurements.

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.

New dataset tests mental rotation from single images, improving model understanding of 3D scenes.

A neural atlas simplifies 3D geometry simulation by avoiding meshing.

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.

Serial section electron microscopy (ssEM) is a widely used technique for obtaining volumetric information of biological tissues at nanometer scale. However, accurate 3D reconstructions of identified cellular structures and volumetric quantifications require precise estimates of section thickness and anisotropy (or stre…

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…

Accurate quantification of pulmonary nodules can greatly assist the early diagnosis of lung cancer, which can enhance patient survival possibilities. A number of nodule segmentation techniques have been proposed, however, all of the existing techniques rely on radiologist 3-D volume of interest (VOI) input or use the c…

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…

We revisit the proof by Qin et al. (2014) of bounded regret of the C$^2$UCB contextual combinatorial bandit. We demonstrate an error in the proof of volumetric expansion of the moment matrix, used in upper bounding a function of context vector norms. We prove a relaxed inequality that yields the originally-stated regre…

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 create synthetic MRI brain scans for research.

The Hodge decomposition provides a very powerful mathematical method for the analysis of 2D and 3D vector fields. It states roughly that any vector field can be $L^2$-orthogonally decomposed into a curl-free, divergence-free, and a harmonic field. The harmonic field itself can be further decomposed into three component…

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.

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…

Paper proves anisotropic Minkowski inequality and related inequalities.

Automated brain tumor segmentation plays an important role in the diagnosis and prognosis of the patient. In addition, features from the tumorous brain help in predicting patients overall survival. The main focus of this paper is to segment tumor from BRATS 2018 benchmark dataset and use age, shape and volumetric featu…

Paper develops a new model for forecasting ocean currents.

The paper introduces various canonical parameterizations for 2D-curved shapes.

There are currently two parameterizations used to derive fixed kernels corresponding to infinite width neural networks, the NTK (Neural Tangent Kernel) parameterization and the naive standard parameterization. However, the extrapolation of both of these parameterizations to infinite width is problematic. The standard p…

This work improves medical image segmentation with limited annotations using contrastive learning.

Dissertation tackles zero-shot anomaly detection, focusing on consistent anomalies and proposing CoDeGraph framework.

We consider asymptotically flat Riemannian manifolds with nonnegative scalar curvature that are conformal to $\R^{n}\setminus Ω, n\ge 3$, and so that their boundary is a minimal hypersurface. (Here, $Ω\subset \R^{n}$ is open bounded with smooth mean-convex boundary.) We prove that the ADM mass of any such manifold is b…

New parameterization for $(1,1)$-knots simplifies their study.

AI tool automates blood segmentation from head CT scans after SAH.

Stochastic parameterizations account for uncertainty in the representation of unresolved sub-grid processes by sampling from the distribution of possible sub-grid forcings. Some existing stochastic parameterizations utilize data-driven approaches to characterize uncertainty, but these approaches require significant str…

The current paper discusses some new results about conformal polynomic surface parameterizations. A new theorem is proved: Given a conformal polynomic surface parameterization of any degree it must be harmonic on each component. As a first geometrical application, every surface that admits a conformal polynomic paramet…

Polynomially parameterizes knots and spheres, proving analogous results.

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…

Conformal surface parameterization is useful in graphics, imaging and visualization, with applications to texture mapping, atlas construction, registration, remeshing and so on. With the increasing capability in scanning and storing data, dense 3D surface meshes are common nowadays. While meshes with higher resolution …

Two novel algorithms for conformal parameterization of multiply-connected surfaces.

The paper analyzes how over-parameterization affects GD convergence in matrix sensing problems.

Novel framework for policy optimization with general parameterization and linear convergence.