Related papers: A trilinear method for finding null points in a 3D…

In the Subspace Clustering with Missing Data (SCMD) problem, we are given a collection of n partially observed d-dimensional vectors. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of SCMD…

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting…

We consider Newton's method for finding zeros of mappings from a manifold $\mathcal X$ into a vector bundle $\mathcal E$. In this setting a connection on $\mathcal E$ is required to render the Newton equation well defined, and a retraction…

When used to accelerate the convergence of fixed-point iterative methods, such as the Picard method, which is a kind of nonlinear fixed-point iteration, polynomial extrapolation techniques can be very effective. The numerical solution of…

Generative 3D reconstruction shows strong potential in incomplete observations. While sparse-view and single-image reconstruction are well-researched, partial observation remains underexplored. In this context, dense views are accessible…

We propose an algorithm based on Newton's method and subdivision for finding all zeros of a polynomial system in a bounded region of the plane. This algorithm can be used to find the intersections between a line and a surface, which has…

This work provides a complete characterization of the solutions of a linear interpolation problem for vector polynomials. The interpolation problem consists in finding n scalar polynomials such that an equation involving a linear…

We propose a new outlier detection method for multi-dimensional data. The method detects outliers based on vector cosine similarity, using a new dataset constructed by adding a dimension with zero values to the original data. When a point…

We consider the problem of identifying n points in the plane using disks, i.e., minimizing the number of disks so that each point is contained in a disk and no two points are in exactly the same set of disks. This problem can be seen as an…

3D object detection with LiDAR point clouds plays an important role in autonomous driving perception module that requires high speed, stability and accuracy. However, the existing point-based methods are challenging to reach the speed…

LiDAR point clouds can effectively depict the motion and posture of objects in three-dimensional space. Many studies accomplish the 3D object detection by voxelizing point clouds. However, in autonomous driving scenarios, the sparsity and…

This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…

The purposes of this paper are to classify lower triangular forms and to determine under what conditions a nonlinear system is equivalent to a specific type of lower triangular forms. According to the least multi-indices and the greatest…

We introduce new methods for integrating nonlinear differential equations on low-rank manifolds. These methods rely on interpolatory projections onto the tangent space, enabling low-rank time integration of vector fields that can be…

This paper presents a new method to recover the relative pose between two images, using three points and the vertical direction information. The vertical direction can be determined in two ways: 1- using direct physical measurement like IMU…

Sparse voxel-based 3D convolutional neural networks (CNNs) are widely used for various 3D vision tasks. Sparse voxel-based 3D CNNs create sparse non-empty voxels from the 3D input and perform 3D convolution operations on them only. We…

This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation…

We introduce a new approach for identifying and characterizing voids within two-dimensional (2D) point distributions through the integration of Delaunay triangulation and Voronoi diagrams, combined with a Minimal Distance Scoring algorithm.…

LiDAR-based 3D object detection is an important task for autonomous driving and current approaches suffer from sparse and partial point clouds of distant and occluded objects. In this paper, we propose a novel two-stage approach, namely…

For autonomous navigation, accurate localization with respect to a map is needed. In urban environments, infrastructure such as buildings or bridges cause major difficulties to Global Navigation Satellite Systems (GNSS) and, despite…