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Graph-based methods have proven to be effective in capturing relationships among points for 3D point cloud analysis. However, these methods often suffer from suboptimal graph structures, particularly due to sparse connections at boundary…
Point Cloud Registration (PCR) is a fundamental and significant issue in photogrammetry and remote sensing, aiming to seek the optimal rigid transformation between sets of points. Achieving efficient and precise PCR poses a considerable…
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…
Several data analysis techniques employ similarity relationships between data points to uncover the intrinsic dimension and geometric structure of the underlying data-generating mechanism. In this paper we work under the model assumption…
Network data, commonly used throughout the physical, social, and biological sciences, consist of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to…
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…
We present a novel hybrid strategy based on machine learning to improve curvature estimation in the level-set method. The proposed inference system couples enhanced neural networks with standard numerical schemes to compute curvature more…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
Recently, several networks that operate directly on point clouds have been proposed. There is significant utility in understanding their mechanisms to classify point clouds, which can potentially help diagnosing these networks and designing…
We propose an auto-encoding network architecture for point clouds (PC) capable of extracting shape signatures without supervision. Building on this, we (i) design a loss function capable of modelling data variance on PCs which are…
In this paper, we propose a normal estimation method for unstructured 3D point clouds. This method, called Nesti-Net, builds on a new local point cloud representation which consists of multi-scale point statistics (MuPS), estimated on a…
In recent years, point cloud representation has become one of the research hotspots in the field of computer vision, and has been widely used in many fields, such as autonomous driving, virtual reality, robotics, etc. Although deep learning…
We present a comprehensive survey and benchmark of both traditional and learning-based methods for surface reconstruction from point clouds. This task is particularly challenging for real-world acquisitions due to factors such as noise,…
Orienting surface normals correctly and consistently is a fundamental problem in geometry processing. Applications such as visualization, feature detection, and geometry reconstruction often rely on the availability of correctly oriented…
Three-dimensional (3D) point cloud analysis has become one of the attractive subjects in realistic imaging and machine visions due to its simplicity, flexibility and powerful capacity of visualization. Actually, the representation of scenes…
We consider the problem of positioning a cloud of points in the Euclidean space $\mathbb{R}^d$, using noisy measurements of a subset of pairwise distances. This task has applications in various areas, such as sensor network localization and…
Estimating surface normals from 3D point clouds is critical for various applications, including surface reconstruction and rendering. While existing methods for normal estimation perform well in regions where normals change slowly, they…
Point clouds and polygonal meshes are widely used when modeling real-world scenarios. Here, point clouds arise, for instance, from acquisition processes applied in various surroundings, such as reverse engineering, rapid prototyping, or…
We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…
Point cloud representation has gained traction due to its efficient memory usage and simplicity in acquisition, manipulation, and storage. However, as point cloud sizes increase, effective down-sampling becomes essential to address the…