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Estimating the normal of a point requires constructing a local patch to provide center-surrounding context, but determining the appropriate neighborhood size is difficult when dealing with different data or geometries. Existing methods…
The generalized winding number (GWN) is a scalar field that supports robust containment queries on curved geometry, including non-watertight, overlapping, and nested boundary representations. While queries can be easily parallelized over…
Anomaly detection based on 3D point cloud data is an important research problem and receives more and more attention recently. Untrained anomaly detection based on only one sample is an emerging research problem motivated by real…
Estimation of surface curvature from range data is important for a range of tasks in computer vision and robotics, object segmentation, object recognition and robotic grasping estimation. This work presents a fast method of robustly…
Estimation of differential geometric quantities in discrete 3D data representations is one of the crucial steps in the geometry processing pipeline. Specifically, estimating normals and sharp feature lines from raw point cloud helps improve…
Point cloud denoising aims to restore clean point clouds from raw observations corrupted by noise and outliers while preserving the fine-grained details. We present a novel deep learning-based denoising model, that incorporates normalizing…
3D dynamic point clouds provide a natural discrete representation of real-world objects or scenes in motion, with a wide range of applications in immersive telepresence, autonomous driving, surveillance, \etc. Nevertheless, dynamic point…
For strongly convex objectives that are smooth, the classical theory of gradient descent ensures linear convergence relative to the number of gradient evaluations. An analogous nonsmooth theory is challenging. Even when the objective is…
Point cloud registration has been one of the basic steps of point cloud processing, which has a lot of applications in remote sensing and robotics. In this report, we summarized the basic workflow of target-less point cloud…
We address the problem of comparing and aligning spatial point configurations in $\mathbb{R}^3$ arising from structured geometric patterns. Each pattern is decomposed into arms along which we define a normalized finite-difference operator…
Pre-trained point cloud analysis models have shown promising advancements in various downstream tasks, yet their effectiveness is typically suffering from low-quality point cloud (i.e., noise and incompleteness), which is a common issue in…
Point clouds are characterized by irregularity and unstructuredness, which pose challenges in efficient data exploitation and discriminative feature extraction. In this paper, we present an unsupervised deep neural architecture called…
In recent years, three-dimensional point clouds are used increasingly to document natural environments. Each dataset contains a diverse set of objects, at varying shapes and sizes, distributed throughout the data and intricately intertwined…
End-to-end trained per-point embeddings are an essential ingredient of any state-of-the-art 3D point cloud processing such as detection or alignment. Methods like PointNet, or the more recent point cloud transformer -- and its variants --…
Many point cloud classification methods are developed under the assumption that all point clouds in the dataset are well aligned with the canonical axes so that the 3D Cartesian point coordinates can be employed to learn features. When…
Point cloud is a collection of 3D coordinates that are discrete geometric samples of an object's 2D surfaces. Imperfection in the acquisition process means that point clouds are often corrupted with noise. Building on recent advances in…
Inspired by the key principle behind the EM algorithm, we propose a general methodology for conducting wavelet estimation with irregularly-spaced data by viewing the data as the observed portion of an augmented regularly-spaced data set. We…
Object point cloud classification has drawn great research attention since the release of benchmarking datasets, such as the ModelNet and the ShapeNet. These benchmarks assume point clouds covering complete surfaces of object instances, for…
Neural operations that rely on neighborhood information are much more expensive when deployed on point clouds than on grid data due to the irregular distances between points in a point cloud. In a grid, on the other hand, we can compute the…
A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…