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Point cloud registration is a key problem for computer vision applied to robotics, medical imaging, and other applications. This problem involves finding a rigid transformation from one point cloud into another so that they align. Iterative…

In recent years new application areas have emerged in which one aims to capture the geometry of objects by means of three-dimensional point clouds. Often the obtained data consist of a dense sampling of the object's surface, containing many…

Point cloud registration is a classical topic in the field of 3D Vision and Computer Graphics. Generally, the implementation of registration is typically sensitive to similarity transformations (translation, scaling, and rotation), noisy…

PointNet has recently emerged as a popular representation for unstructured point cloud data, allowing application of deep learning to tasks such as object detection, segmentation and shape completion. However, recent works in literature…

We consider the optimization problem with a generally quadratic matrix constraint of the form $X^TAX = J$, where $A$ is a given nonsingular, symmetric $n\times n$ matrix and $J$ is a given $k\times k$ symmetric matrix, with $k\leq n$,…

This paper addresses a class of nonsmooth and nonconvex optimization problems defined on complete Riemannian manifolds. The objective function has a composite structure, combining convex, differentiable, and lower semicontinuous terms,…

We analyze the problem of determining whether 2 given point clouds in 2D, with any distinct cardinality and any number of outliers, have subsets of the same size that can be matched via a rigid motion. This problem is important, for…

Learning-based point cloud registration methods can handle clean point clouds well, while it is still challenging to generalize to noisy, partial, and density-varying point clouds. To this end, we propose a novel point cloud registration…

We present a novel method for reconstructing parametric, volumetric, multi-story building models from unstructured, unfiltered indoor point clouds by means of solving an integer linear optimization problem. Our approach overcomes…

This paper concerns the research problem of point cloud registration to find the rigid transformation to optimally align the source point set with the target one. Learning robust point cloud registration models with deep neural networks has…

Point cloud registration is the task of estimating the rigid transformation that aligns a pair of point cloud fragments. We present an efficient and robust framework for pairwise registration of real-world 3D scans, leveraging Hough voting…

Point cloud registration is a fundamental problem in 3D computer vision, graphics and robotics. For the last few decades, existing registration algorithms have struggled in situations with large transformations, noise, and time constraints.…

We study the problem of finding the global Riemannian center of mass of a set of data points on a Riemannian manifold. Specifically, we investigate the convergence of constant step-size gradient descent algorithms for solving this problem.…

This paper presents a robust probabilistic point registration method for estimating the rigid transformation (i.e. rotation matrix and translation vector) between two pointcloud dataset. The method improves the robustness of point…

Semantic shape completion is a challenging problem in 3D computer vision where the task is to generate a complete 3D shape using a partial 3D shape as input. We propose a learning-based approach to complete incomplete 3D shapes through…

Robust Affine Matching with Grassmannians (RoAM) is a new algorithm to perform affine registration of point clouds. The algorithm is based on minimizing the Frobenius distance between two elements of the Grassmannian. For this purpose, an…

Point clouds are an increasingly relevant data type but they are often corrupted by noise. We propose a deep neural network based on graph-convolutional layers that can elegantly deal with the permutation-invariance problem encountered by…

We investigate a variation of the 3D registration problem, named multi-model 3D registration. In the multi-model registration problem, we are given two point clouds picturing a set of objects at different poses (and possibly including…

This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…

Under the data manifold hypothesis, high-dimensional data are concentrated near a low-dimensional manifold. We study the problem of Riemannian optimization over such manifolds when they are given only implicitly through the data…