arXiv research

Estimates for $p$-capacities on symmetric manifolds.

New method beats volumetric barrier for manifold recovery.

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

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

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…

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

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.

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

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…

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 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…

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…

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…

A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe. Galaxy surveys provide the means to map out cosmic large-scale structure in thr…

The paper proves a new inequality linking mass and volume in 3D space.

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…

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…

The paper models quanto weather and energy derivatives using Ornstein-Uhlenbeck processes and develops methods to hedge them.

Paper develops a new model for forecasting ocean currents.

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…

Novel framework predicts brain biomarker trajectories with superior performance.

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 …

We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of brain summary measures (volumetric and cortical thickness values) to single nucleo…

Jointly estimates flow fields and particle properties from Lagrangian data.

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

In this work we propose an adversarial learning approach to generate high resolution MRI scans from low resolution images. The architecture, based on the SRGAN model, adopts 3D convolutions to exploit volumetric information. For the discriminator, the adversarial loss uses least squares in order to stabilize the traini…

LU-Net improves cardiac segmentation accuracy and robustness.

Deep neural networks map brain lesions to deficits for better brain function understanding.

The ability of having a sparse representation for a certain class of signals has many applications in data analysis, image processing, and other research fields. Among sparse representations, the cosparse analysis model has recently gained increasing interest. Many signals exhibit a multidimensional structure, e.g. ima…

Graph refinement, or the task of obtaining subgraphs of interest from over-complete graphs, can have many varied applications. In this work, we extract trees or collection of sub-trees from image data by, first deriving a graph-based representation of the volumetric data and then, posing the tree extraction as a graph …