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The computation of Voronoi Diagrams, or their dual Delauney triangulations is difficult in high dimensions. In a recent publication Polianskii and Pokorny propose an iterative randomized algorithm facilitating the approximation of Voronoi…
We consider regularized cutting-plane methods to minimize a convex function that is the sum of a large number of component functions. One important example is the dual problem obtained from Lagrangian relaxation on a decomposable problem.…
We present a simple algorithm for computing higher-order Delaunay mosaics that works in Euclidean spaces of any finite dimensions. The algorithm selects the vertices of the order-$k$ mosaic from incrementally constructed lower-order mosaics…
Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…
The point inclusion tests for polygons, in other words the point-in-polygon (PIP) algorithms, are fundamental tools for many scientific fields related to computational geometry, and they have been studied for a long time. The PIP algorithms…
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…
The task of point cloud upsampling aims to acquire dense and uniform point sets from sparse and irregular point sets. Although significant progress has been made with deep learning models, state-of-the-art methods require ground-truth dense…
We investigate ways in which an algorithm can improve its expected performance by fine-tuning itself automatically with respect to an unknown input distribution D. We assume here that D is of product type. More precisely, suppose that we…
We present the DTFE public software, a code for reconstructing fields from a discrete set of samples/measurements using the maximum of information contained in the point distribution. The code is written in C++ using the CGAL library and is…
Point cloud upsampling aims to generate dense and uniformly distributed point sets from sparse point clouds. Existing point cloud upsampling methods typically approach the task as an interpolation problem. They achieve upsampling by…
The survey volume of a proper motion-limited sample is typically much smaller than a magnitude-limited sample. This is because of the noisy astrometric measurements from detectors that are not dedicated for astrometric missions. In order to…
Data augmentation refers to the process of applying a series of transformations or expansions to original data to generate new samples, thereby increasing the diversity and quantity of the data, effectively improving the performance and…
Traditional algorithms of point set registration minimizing point-to-plane distances often achieve a better estimation of rigid transformation than those minimizing point-to-point distances. Nevertheless, recent deep-learning-based methods…
Digital Elevation Models (DEMs) are important datasets for modelling the line of sight, such as radio signals, sound waves and human vision. These are commonly analyzed using rotational sweep algorithms. However, such algorithms require…
We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…
One established metric to classify the significance of a mountain peak is its isolation. It specifies the distance between a peak and the closest point of higher elevation. Peaks with high isolation dominate their surroundings and provide a…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
Higher order cumulants of point processes, such as skew and kurtosis, require significant computational effort to calculate. The traditional counts-in-cells method implicitly requires a large amount of computation since, for each sampling…
Airplane refueling problem is a nonlinear unconstrained optimization problem with $n!$ feasible solutions. Given a fleet of $n$ airplanes with mid-air refueling technique, the question is to find the best refueling policy to make the last…
Algorithms for extracting hydrologic features and properties from digital elevation models (DEMs) are challenged by large datasets, which often cannot fit within a computer's RAM. Depression filling is an important preconditioning step to…