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Anomaly detection is the process of identifying abnormal instances or events in data sets which deviate from the norm significantly. In this study, we propose a signatures based machine learning algorithm to detect rare or unexpected items…

Point clouds have attracted increasing attention. Significant progress has been made in methods for point cloud analysis, which often requires costly human annotation as supervision. To address this issue, we propose a novel…

Recognition of occluded objects in unseen indoor environments is a challenging problem for mobile robots. This work proposes a new slicing-based topological descriptor that captures the 3D shape of object point clouds to address this…

In this paper, we present Position-to-Structure Attention Transformers (PS-Former), a Transformer-based algorithm for 3D point cloud recognition. PS-Former deals with the challenge in 3D point cloud representation where points are not…

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension.…

Existing position based point cloud filtering methods can hardly preserve sharp geometric features. In this paper, we rethink point cloud filtering from a non-learning non-local non-normal perspective, and propose a novel position based…

One of basic difficulties of machine learning is handling unknown rotations of objects, for example in image recognition. A related problem is evaluation of similarity of shapes, for example of two chemical molecules, for which direct…

Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for orthogonal and symplectic random matrix ensembles. Motivated by the average of characteristic polynomials of the Bures random matrix ensemble…

We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing…

Learning to predict reliable characteristic orientations of 3D point clouds is an important yet challenging problem, as different point clouds of the same class may have largely varying appearances. In this work, we introduce a novel method…

The irregularity and permutation invariance of point cloud data pose challenges for effective learning. Conventional methods for addressing this issue involve converting raw point clouds to intermediate representations such as 3D voxel…

We investigate the representation of symmetric polynomials as a sum of squares. Since this task is solved using semidefinite programming tools we explore the geometric, algebraic, and computational implications of the presence of discrete…

Preprocessing a 2D image often produces a noisy cloud of interest points. We study the problem of counting holes in unorganized clouds in the plane. The holes in a given cloud are quantified by the topological persistence of their boundary…

The majority of point cloud registration methods currently rely on extracting features from points. However, these methods are limited by their dependence on information obtained from a single modality of points, which can result in…

Point cloud processing is a challenging task due to its sparsity and irregularity. Prior works introduce delicate designs on either local feature aggregator or global geometric architecture, but few combine both advantages. We propose…

We study the problem of how many different sums of squares decompositions a general polynomial $f$ with SOS-rank $k$ admits. We show that there is a link between the variety $\mathrm{SOS}_k(f)$ of all SOS-decompositions of $f$ and the…

For both indoor and outdoor environments, we propose an efficient and novel method for different scales and sparse 3D point clouds registration that cannot be handled by the current popular ICP approaches. Our algorithm efficiently detects…

The success of deep learning methods led to significant breakthroughs in 3-D point cloud processing tasks with applications in remote sensing. Existing methods utilize convolutions that have some limitations, as they assume a uniform input…

Processing large point clouds is a challenging task. Therefore, the data is often sampled to a size that can be processed more easily. The question is how to sample the data? A popular sampling technique is Farthest Point Sampling (FPS).…

Point cloud registration is crucial for ensuring 3D alignment consistency of multiple local point clouds in 3D reconstruction for remote sensing or digital heritage. While various point cloud-based registration methods exist, both…