Related papers: Feature Curves and Surfaces of 3D Asymmetric Tenso…

It is shown that small externally applied magnetic perturbations can significantly alter important geometric properties of magnetic flux surfaces in tokamaks. Through 3D shaping, experimentally relevant perturbation levels are large enough…

Accurate reconstruction of leaf surfaces from 3D point cloud is essential for agricultural applications such as phenotyping. However, real-world plant data (i.e., irregular 3D point cloud) are often complex to reconstruct plant parts…

Superconductors with nontrivial band structure topology represent a class of materials with unconventional and potentially useful properties. Recent years have seen much success in creating artificial hybrid structures exhibiting main…

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or…

The tensor power method generalizes the matrix power method to higher order arrays, or tensors. Like in the matrix case, the fixed points of the tensor power method are the eigenvectors of the tensor. While every real symmetric matrix has…

The purpose of this paper is to study the problem of computing unitary eigenvalues (U-eigenvalues) of non-symmetric complex tensors. By means of symmetric embedding of complex tensors, the relationship between U-eigenpairs of a…

Deep neural networks for 3D point cloud understanding have achieved remarkable success in object classification and recognition, yet recent work shows that these models remain highly vulnerable to adversarial perturbations. Existing 3D…

In this paper, we introduce a novel parametric method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D…

Recent advances in 3D deep learning have shown that it is possible to train highly effective deep models for 3D shape generation, directly from 2D images. This is particularly interesting since the availability of 3D models is still limited…

Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or…

Vector fields are widely used to represent and model flows for many science and engineering applications. This paper introduces a novel neural network architecture for learning tangent vector fields that are intrinsically defined on…

The detection of vascular structures from noisy images is a fundamental process for extracting meaningful information in many applications. Most well-known vascular enhancing techniques often rely on Hessian-based filters. This paper…

This paper introduces a generative model for 3D surfaces based on a representation of shapes with mean curvature and metric, which are invariant under rigid transformation. Hence, compared with existing 3D machine learning frameworks, our…

Feature extraction for tensor data serves as an important step in many tasks such as anomaly detection, process monitoring, image classification, and quality control. Although many methods have been proposed for tensor feature extraction,…

In recent years, the use of expressive surface visualizations in the representation of vascular structures has gained significant attention. These visualizations provide a comprehensive understanding of complex anatomical structures and are…

Geometric metrology includes one or two-dimensional (1D or 2D) distance or plane measurements, as well as the three-dimensional (3D) scanning. The 1D or 2D measuring system is unable to obtain advanced 3D feature, while the 3D scanning…

This paper discusses the problem of symmetric tensor decomposition on a given variety $X$: decomposing a symmetric tensor into the sum of tensor powers of vectors contained in $X$. In this paper, we first study geometric and algebraic…

Most 3D shape analysis methods use triangular meshes to discretize both the shape and functions on it as piecewise linear functions. With this representation, shape analysis requires fine meshes to represent smooth shapes and geometric…

Implicit fields have recently shown increasing success in representing and learning 3D shapes accurately. Signed distance fields and occupancy fields are decades old and still the preferred representations, both with well-studied…

In this note, we consider the highly nonconvex optimization problem associated with computing the rank decomposition of symmetric tensors. We formulate the invariance properties of the loss function and show that critical points detected by…