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Point cloud registration plays a critical role in a multitude of computer vision tasks, such as pose estimation and 3D localization. Recently, a plethora of deep learning methods were formulated that aim to tackle this problem. Most of…

This paper considers a stochastic optimization problem over the fixed point sets of quasinonexpansive mappings on Riemannian manifolds. The problem enables us to consider Riemannian hierarchical optimization problems over complicated sets,…

This paper considers the optimization problem in the form of $\min_{X \in \mathcal{F}_v} f(x) + \lambda \|X\|_1,$ where $f$ is smooth, $\mathcal{F}_v = \{X \in \mathbb{R}^{n \times q} : X^T X = I_q, v \in \mathrm{span}(X)\}$, and $v$ is a…

A quasi-Newton method with cubic regularization is designed for solving Riemannian unconstrained nonconvex optimization problems. The proposed algorithm is fully adaptive with at most ${\cal O} (\epsilon_g^{-3/2})$ iterations to achieve a…

Point cloud registration aligns multiple unposed point clouds into a common reference frame and is a core step for 3D reconstruction and robot localization without initial guess. In this work, we cast registration as conditional generation:…

In this paper, we propose a coarse-to-fine integration solution inspired by the classical ICP algorithm, to pairwise 3D point cloud registration with two improvements of hybrid metric spaces (eg, BSC feature and Euclidean geometry spaces)…

This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a…

Point cloud rigid registration is a fundamental problem in 3D computer vision. In the multiview case, we aim to find a set of 6D poses to align a set of objects. Methods based on pairwise registration rely on a subsequent synchronization…

We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…

We propose a new framework that formulates point cloud registration as a denoising diffusion process from noisy transformation to object transformation. During training stage, object transformation diffuses from ground-truth transformation…

Point clouds registration is a fundamental step of many point clouds processing pipelines; however, most algorithms are tested on data that are collected ad-hoc and not shared with the research community. These data often cover only a very…

Recently, many deep neural networks were designed to process 3D point clouds, but a common drawback is that rotation invariance is not ensured, leading to poor generalization to arbitrary orientations. In this paper, we introduce a new…

Point cloud analysis is an area of increasing interest due to the development of 3D sensors that are able to rapidly measure the depth of scenes accurately. Unfortunately, applying deep learning techniques to perform point cloud analysis is…

We propose DeepMapping, a novel registration framework using deep neural networks (DNNs) as auxiliary functions to align multiple point clouds from scratch to a globally consistent frame. We use DNNs to model the highly non-convex mapping…

We propose a new method for fine registering multiple point clouds simultaneously. The approach is characterized by being dense, therefore point clouds are not reduced to pre-selected features in advance. Furthermore, the approach is robust…

The Procrustes-Wasserstein problem consists in matching two high-dimensional point clouds in an unsupervised setting, and has many applications in natural language processing and computer vision. We consider a planted model with two…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

Point cloud registration involves determining a rigid transformation to align a source point cloud with a target point cloud. This alignment is fundamental in applications such as autonomous driving, robotics, and medical imaging, where…

Given the prominence of current 3D sensors, a fine-grained analysis on the basic point cloud data is worthy of further investigation. Particularly, real point cloud scenes can intuitively capture complex surroundings in the real world, but…

In this paper, we propose a point cloud classification method based on graph neural network and manifold learning. Different from the conventional point cloud analysis methods, this paper uses manifold learning algorithms to embed point…