相关论文: Sorting out typicality with the inverse moment mat…
Handling an infinite number of inequality constraints in infinite-dimensional spaces occurs in many fields, from global optimization to optimal transport. These problems have been tackled individually in several previous articles through…
This paper researches the unexplored task-point cloud salient object detection (SOD). Differing from SOD for images, we find the attention shift of point clouds may provoke saliency conflict, i.e., an object paradoxically belongs to salient…
The dynamics of many systems from physics, economics, chemistry, and biology can be modelled through polynomial functions. In this paper, we provide a computational means to find positively invariant sets of polynomial dynamical systems by…
We study sum of squares (SOS) relaxations to optimize polynomial functions over a set $V\cap R^n$, where $V$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description, represents…
This work proposes and investigates a novel method for anomaly detection and shows it to be competitive in a variety of Euclidean and non-Euclidean situations. It is based on an extension of the depth quantile functions (DQF) approach. The…
Persistence diagrams have been widely recognized as a compact descriptor for characterizing multiscale topological features in data. When many datasets are available, statistical features embedded in those persistence diagrams can be…
Polynomial ensembles are determinantal point processes associated with (non necessarily orthogonal) projections onto polynomial subspaces. The aim of this survey article is to put forward the use of recurrence coefficients to obtain the…
We propose the use of a Transformer to accurately predict normals from point clouds with noise and density variations. Previous learning-based methods utilize PointNet variants to explicitly extract multi-scale features at different input…
In this work, we tackle the task of estimating the 6D pose of an object from point cloud data. While recent learning-based approaches to addressing this task have shown great success on synthetic datasets, we have observed them to fail in…
Skew orthogonal polynomials arise in the calculation of the $n$-point distribution function for the eigenvalues of ensembles of random matrices with orthogonal or symplectic symmetry. In particular, the distribution functions are completely…
This paper introduces a notion of decomposition and completion of sum-of-squares (SOS) matrices. We show that a subset of sparse SOS matrices with chordal sparsity patterns can be equivalently decomposed into a sum of multiple SOS matrices…
As 3D scanning devices and depth sensors mature, point clouds have attracted increasing attention as a format for 3D object representation, with applications in various fields such as tele-presence, navigation and heritage reconstruction.…
In recent years, deep learning-based point cloud normal estimation has made great progress. However, existing methods mainly rely on the PCPNet dataset, leading to overfitting. In addition, the correlation between point clouds with…
Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condition for nonnegativity is the Sum of Squares (SOS) property,…
An exploit of the Sequential Importance Sampling (SIS) algorithm using Differential Algebra (DA) techniques is derived to develop an efficient particle filter. The filter creates an original kind of particles, called scout particles, that…
We derive bulk asymptotics of skew-orthogonal polynomials (sop) $\pi^{\bt}_{m}$, $\beta=1$, 4, defined w.r.t. the weight $\exp(-2NV(x))$, $V (x)=gx^4/4+tx^2/2$, $g>0$ and $t<0$. We assume that as $m,N \to\infty$ there exists an $\epsilon >…
The points on the point clouds that can entirely outline the shape of the model are of critical importance, as they serve as the foundation for numerous point cloud processing tasks and are widely utilized in computer graphics and…
Monitoring network traffic data to detect any hidden patterns of anomalies is a challenging and time-consuming task that requires high computing resources. To this end, an appropriate summarization technique is of great importance, where it…
We present a hierarchy of semidefinite programs (SDPs) for the problem of fitting a shape-constrained (multivariate) polynomial to noisy evaluations of an unknown shape-constrained function. These shape constraints include convexity or…
3D object detection from point clouds plays a critical role in autonomous driving. Currently, the primary methods for point cloud processing are voxel-based and pillar-based approaches. Voxel-based methods offer high accuracy through…