Related papers: Registration of algebraic varieties using Riemanni…

The task of image restration is to find the spatial correspondence of two or more given images. In this paper we assume that the correspondence is given either by an Euclidean, or by an affine volume-preserving transformation. Since the…

Riemannian optimization is concerned with problems, where the independent variable lies on a smooth manifold. There is a number of problems from numerical linear algebra that fall into this category, where the manifold is usually specified…

We study the problem of extracting accurate correspondences for point cloud registration. Recent keypoint-free methods bypass the detection of repeatable keypoints which is difficult in low-overlap scenarios, showing great potential in…

Estimating the rigid transformation between two LiDAR scans through putative 3D correspondences is a typical point cloud registration paradigm. Current 3D feature matching approaches commonly lead to numerous outlier correspondences, making…

We focus on the problem of class-agnostic instance segmentation of LiDAR point clouds. We propose an approach that combines graph-theoretic search with data-driven learning: it searches over a set of candidate segmentations and returns one…

Deep neural networks endow the downsampled superpoints with highly discriminative feature representations. Previous dominant point cloud registration approaches match these feature representations as the first step, e.g., using the Sinkhorn…

A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix…

Point clouds are a fundamental representation for robotic perception tasks such as localization, mapping, and object pose estimation. However, LiDAR-acquired point clouds are inherently sparse and non-uniform, providing incomplete…

Riemannian geometry provides the fundamental framework for optimization on nonlinear spaces such as matrix manifolds, which arise in machine learning, signal processing, and robotics. While the underlying theory is classical, existing…

Optimization with orthogonality constraints frequently arises in various fields such as machine learning. Riemannian optimization offers a powerful framework for solving these problems by equipping the constraint set with a Riemannian…

Shape registration is the process of aligning one 3D model to another. Most previous methods to align shapes with no known correspondences attempt to solve for both the transformation and correspondences iteratively. We present a shape…

The problem of determining the configuration of points from partial distance information, known as the Euclidean Distance Geometry (EDG) problem, is fundamental to many tasks in the applied sciences. In this paper, we propose two algorithms…

As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…

We develop new algorithms for Riemannian bilevel optimization. We focus in particular on batch and stochastic gradient-based methods, with the explicit goal of avoiding second-order information such as Riemannian hyper-gradients. We propose…

As a fundamental yet challenging problem in intelligent transportation systems, point cloud registration attracts vast attention and has been attained with various deep learning-based algorithms. The unsupervised registration algorithms…

We propose an extremely versatile approach to address a large family of matrix nearness problems, possibly with additional linear constraints. Our method is based on splitting a matrix nearness problem into two nested optimization problems,…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

Multi-view point cloud registration is fundamental in 3D reconstruction. Since there are close connections between point clouds captured from different viewpoints, registration performance can be enhanced if these connections be harnessed…

Point-set registration is a classical image processing problem that looks for the optimal transformation between two sets of points. In this work, we analyze the impact of outliers when finding the optimal rotation between two point clouds.…

Many types of 3D acquisition sensors have emerged in recent years and point cloud has been widely used in many areas. Accurate and fast registration of cross-source 3D point clouds from different sensors is an emerged research problem in…