Related papers: Sorting out typicality with the inverse moment mat…

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…

Given partial objects and some complete ones as references, point cloud completion aims to recover authentic shapes. However, existing methods pay little attention to general shapes, which leads to the poor authenticity of completion…

We consider Holder smoothness classes of surfaces for which we construct piecewise polynomial approximation networks, which are graphs with polynomial pieces as nodes and edges between polynomial pieces that are in `good continuation' of…

This paper presents a new approach, based on polynomial optimization and the method of moments, to the problem of anomaly detection. The proposed technique only requires information about the statistical moments of the normal-state…

This paper investigates multi-scale feature approximation and transferable features for object detection from point clouds. Multi-scale features are critical for object detection from point clouds. However, multi-scale feature learning…

Contrastive representation learning has emerged as an outstanding approach for anomaly detection. In this work, we explore the $\ell_2$-norm of contrastive features and its applications in out-of-distribution detection. We propose a simple…

In this work we introduce a novel adaptive anomaly detection framework specifically designed for monitoring sequential random finite set (RFS) observations. Our approach effectively distinguishes between In-Control data (normal) and…

Instance segmentation in point clouds is one of the most fine-grained ways to understand the 3D scene. Due to its close relationship to semantic segmentation, many works approach these two tasks simultaneously and leverage the benefits of…

We use tropicalization to study the duals to cones of nonnegative polynomials and sums of squares on a semialgebraic set $S$. The truncated cones of moments of measures supported on the set $S$ is dual to nonnegative polynomials on $S$,…

Multivariate orthogonal polynomials in $D$ real dimensions are considered from the perspective of the Cholesky factorization of a moment matrix. The approach allows for the construction of corresponding multivariate orthogonal polynomials,…

This paper presents an effective normal estimation method adopting multi-patch stitching for an unstructured point cloud. The majority of learning-based approaches encode a local patch around each point of a whole model and estimate the…

This paper introduces a new method for 3D point cloud registration based on deep learning. The architecture is composed of three distinct blocs: (i) an encoder composed of a convolutional graph-based descriptor that encodes the immediate…

Current multi-object tracking and segmentation (MOTS) methods follow the tracking-by-detection paradigm and adopt convolutions for feature extraction. However, as affected by the inherent receptive field, convolution based feature…

Segmenting object instances is a key task in machine perception, with safety-critical applications in robotics and autonomous driving. We introduce a novel approach to instance segmentation that jointly leverages measurements from multiple…

We analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which involves the outward normal derivatives on the sphere. Using their representation in terms of spherical harmonics, algebraic and…

Point clouds are gaining prominence as a method for representing 3D shapes, but their irregular structure poses a challenge for deep learning methods. In this paper we propose CloudWalker, a novel method for learning 3D shapes using random…

We develop a general framework to significantly reduce the degree of sum-of-squares proofs by introducing new variables. To illustrate the power of this framework, we use it to speed up previous algorithms based on sum-of-squares for two…

Humans excel at detecting interesting patterns in images, for example those taken from satellites. This kind of anecdotal evidence can lead to the discovery of new phenomena. However, it is often difficult to gather enough data of…

We consider the problem of computing exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP) solvers. We provide a hybrid numeric-symbolic algorithm…

We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless…