Related papers: Robust Containment Queries over Collections of Rat…

We propose a containment query that is robust to the watertightness of regions bound by trimmed NURBS surfaces, as this property is difficult to guarantee for in-the-wild CAD models. Containment is determined through the generalized winding…

Point containment queries on trimmed surfaces are fundamental to CAD modeling, solid geometry processing, and surface tessellation. Existing approaches such as ray casting and generalized winding numbers often face limitations in robustness…

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…

The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…

This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it…

We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g.,…

Generalized winding numbers provide a robust measure of point insidedness for 3D surfaces - whether open, self-intersecting, or non-manifold - and are central to numerous geometry processing tasks. However, existing methods trade off…

Estimating consistently oriented normals for point clouds enables a number of important applications in computer graphics. While local normal estimation is possible with simple techniques like PCA, orienting them to be globally consistent…

Many clustering algorithms when the data are curves or functions have been recently proposed. However, the presence of contamination in the sample of curves can influence the performance of most of them. In this work we propose a robust,…

An algorithm is proposed for generalized mean curvature flow of closed two-dimensional surfaces, which include inverse mean curvature flow, powers of mean and inverse mean curvature flow, etc. Error estimates are proven for semi- and full…

Compressing a set of unordered points is far more challenging than compressing images/videos of regular sample grids, because of the difficulties in characterizing neighboring relations in an irregular layout of points. Many researchers…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

We propose to explore the properties of raw point clouds through the \emph{winding clearness}, a concept we first introduce for measuring the clarity of the interior/exterior relationships represented by the winding number field of the…

Feature descriptors of point clouds are used in several applications, such as registration and part segmentation of 3D point clouds. Learning discriminative representations of local geometric features is unquestionably the most important…

Deep networks have recently been shown to be vulnerable to universal perturbations: there exist very small image-agnostic perturbations that cause most natural images to be misclassified by such classifiers. In this paper, we propose the…

Learning a latent embedding to understand the underlying nature of data distribution is often formulated in Euclidean spaces with zero curvature. However, the success of the geometry constraints, posed in the embedding space, indicates that…

Estimating normals with globally consistent orientations for a raw point cloud has many downstream geometry processing applications. Despite tremendous efforts in the past decades, it remains challenging to deal with an unoriented point…

Polygonal mesh reconstruction of a raw point cloud is a valuable topic in the field of computer graphics and 3D vision. Especially to 3D architectural models, polygonal mesh provides concise expressions for fundamental geometric structures…

Weighted counting problems are a natural generalization of counting problems where a weight is associated with every computational path of polynomial-time non-deterministic Turing machines and the goal is to compute the sum of the weights…

Matching 3D rigid point clouds in complex environments robustly and accurately is still a core technique used in many applications. This paper proposes a new architecture combining error estimation from sample covariances and dual global…