相关论文: Sorting out typicality with the inverse moment mat…

The standard moment-sum-of-squares (SOS) hierarchy is a powerful method for solving global polynomial optimization problems. However, its convergence relies on Putinar's Positivstellensatz, which requires the feasible set to satisfy the…

Point cloud is a principal data structure adopted for 3D geometric information encoding. Unlike other conventional visual data, such as images and videos, these irregular points describe the complex shape features of 3D objects, which makes…

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 briefly recall basics of the Moment-SOS hierarchy in polynomial optimization and the Christoffel-Darboux kernel (and the Christoffel function (CF)) in theory of approximation and orthogonal polynomials. We then (i) show a strong link…

Point cloud synthesis, i.e. the generation of novel point clouds from an input distribution, remains a challenging task, for which numerous complex machine learning models have been devised. We develop a novel method that encodes…

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…

A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…

We propose an algorithm to select parameter subset combinations that can be estimated using an ordinary least-squares (OLS) inverse problem formulation with a given data set. First, the algorithm selects the parameter combinations that…

In this paper, we investigate the convergence properties of Fourier partial sums associated with general orthonormal systems, focusing on functions that belong to specific differentiable function classes. While classical Fourier analysis…

We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new…

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…

Point cloud completion, which aims at recovering original shape information from partial point clouds, has attracted attention on 3D vision community. Existing methods usually succeed in completion for standard shape, while failing to…

This paper proposes a novel point-cloud-based place recognition system that adopts a deep learning approach for feature extraction. By using a convolutional neural network pre-trained on color images to extract features from a range image…

This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with…

This paper establishes the consistency of spectral approaches to data clustering. We consider clustering of point clouds obtained as samples of a ground-truth measure. A graph representing the point cloud is obtained by assigning weights to…

The paper presents a simple and effective learning-based method for computing a discriminative 3D point cloud descriptor for place recognition purposes. Recent state-of-the-art methods have relatively complex architectures such as…

We introduce an interpolation--regression operator for polynomial approximation on the unit sphere $\mathbb{S}^2$ from discrete samples. The approximant is a spherical polynomial of degree $r$ which interpolates the data on a prescribed…

Point cloud anomaly detection under the anomaly-free setting poses significant challenges as it requires accurately capturing the features of 3D normal data to identify deviations indicative of anomalies. Current efforts focus on devising…

We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids…

This paper addresses the task of estimating the 6 degrees of freedom pose of a known 3D object from depth information represented by a point cloud. Deep features learned by convolutional neural networks from color information have been the…