Related papers: Delaunay Bifiltrations of Functions on Point Cloud…
Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw…
3D point clouds directly collected from objects through sensors are often incomplete due to self-occlusion. Conventional methods for completing these partial point clouds rely on manually organized training sets and are usually limited to…
Divide-and-conquer is a central paradigm for the design of algorithms, through which some fundamental computational problems, such as sorting arrays and computing convex hulls, are solved in optimal time within $\Theta(n\log{n})$ in the…
Point cloud completion estimates complete shapes from incomplete point clouds to obtain higher-quality point cloud data. Most existing methods only consider global object features, ignoring spatial and semantic information of adjacent…
Diffusion models are rapidly redefining 3D anomaly detection in point cloud data. As 3D sensing becomes integral to modern manufacturing, reliable anomaly detection is essential for high-throughput quality assurance and process control. Yet…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
We present the plane-sweep incremental algorithm, a hybrid approach for computing Delaunay tessellations of large point sets whose size exceeds the computer's main memory. This approach unites the simplicity of the incremental algorithms…
As the basic task of point cloud analysis, classification is fundamental but always challenging. To address some unsolved problems of existing methods, we propose a network that captures geometric features of point clouds for better…
In this work, we present a mathematical formulation for machine learning of (1) functions on symmetric matrices that are invariant with respect to the action of permutations by conjugation, and (2) functions on point clouds that are…
Point clouds are a basic data type that is increasingly of interest as 3D content becomes more ubiquitous. Applications using point clouds include virtual, augmented, and mixed reality and autonomous driving. We propose a more efficient…
We apply state-of-the-art computational geometry methods to the problem of reconstructing a time-varying sea surface from tide gauge records. Our work builds on a recent article by Nitzke et al.~(Computers \& Geosciences, 157:104920, 2021)…
We present a robust and fast algorithm for performing astrometry and source cross-identification on two dimensional point lists, such as between a catalogue and an astronomical image, or between two images. The method is based on minimal…
We present a simple and general framework for feature learning from point clouds. The key to the success of CNNs is the convolution operator that is capable of leveraging spatially-local correlation in data represented densely in grids…
Patterns of different symmetries may arise after solution to reaction-diffusion equations. Hexagonal arrays, layers and their perturbations are observed in different models after numerical solution to the corresponding initial-boundary…
Existing networks directly learn feature representations on 3D point clouds for shape analysis. We argue that 3D point clouds are highly redundant and hold irregular (permutation-invariant) structure, which makes it difficult to achieve…
We propose a novel segmentation-based explainable artificial intelligence (XAI) method for neural networks working on point cloud classification. As one building block of this method, we propose a novel point-shifting mechanism to introduce…
Three-dimensional data have become increasingly present in earth observation over the last decades. However, many 3D surveys are still underexploited due to the lack of accessible and explainable automatic classification methods, for…
Point clouds are a fundamental 3D representation in computer vision, enabling a wide range of perception tasks. However, real-world point clouds often suffer from degradations such as incompleteness, noise, outliers, and irregular density,…
Existing deep learning methods for the reconstruction and denoising of point clouds rely on small datasets of 3D shapes. We circumvent the problem by leveraging deep learning methods trained on billions of images. We propose a method to…
Dataset Distillation (DD) aims to distill knowledge from extensive datasets into more compact ones while preserving performance on the test set, thereby reducing storage costs and training expenses. However, existing methods often suffer…