Related papers: Exact computation of the halfspace depth
We introduce a new algorithm for the calculation of multidimensional optical depths in approximate radiative transport schemes, equally applicable to neutrinos and photons. Motivated by (but not limited to) neutrino transport in…
Detecting and masking cloud and cloud shadow from satellite remote sensing images is a pervasive problem in the remote sensing community. Accurate and efficient detection of cloud and cloud shadow is an essential step to harness the value…
In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…
Tukey depth function is one of the most famous multivariate tools serving robust purposes. It is also very well known for its computability problems in dimensions $p \ge 3$. In this paper, we address this computing issue by presenting two…
The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…
This paper addresses the task of estimating the 6 degrees of freedom pose of a known 3D object from depth information represented by a point cloud. Deep features learned by convolutional neural networks from color information have been the…
We compute the maximal halfspace depth for a class of permutation-invariant distributions on the probability simplex. The derivations are based on stochastic ordering results that so far were only showed to be relevant for the…
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…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
Neural networks have shown great success in extracting geometric information from color images. Especially, monocular depth estimation networks are increasingly reliable in real-world scenes. In this work we investigate the applicability of…
We give an exposition of Natural Topology (NToP), which highlights its advantages for exact computation. The NToP-definition of the real numbers (and continuous real functions) matches recent expert recommendations for exact real…
The diameter of a graph is among its most basic parameters. Since a few years, it moreover became a key issue to compute it for massive graphs in the context of complex network analysis. However, known algorithms, including the ones…
Clustering high-dimensional datasets is hard because interpoint distances become less informative in high-dimensional spaces. We present a clustering algorithm that performs nonlinear dimensionality reduction and clustering jointly. The…
This work proposes a method for depth completion of sparse LiDAR data using a convolutional neural network which can be used to generate semi-dense depth maps and "almost" full 3D point-clouds with significantly lower root mean squared…
Frequently, data in scientific computing is in its abstract form a finite point set in space, and it is sometimes useful or required to compute what one might call the ``shape'' of the set. For that purpose, this paper introduces the formal…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
We present a new algorithm to calculate exact hypervolumes. Given a set of $d$-dimensional points, it computes the hypervolume of the dominated space. Determining this value is an important subroutine of Multiobjective Evolutionary…
Given a generic semidefinite program, specified by matrices with rational entries, each coordinate of its optimal solution is an algebraic number. We study the degree of the minimal polynomials of these algebraic numbers. Geometrically,…
Deep neural networks have enabled progress in a wide variety of applications. Growing the size of the neural network typically results in improved accuracy. As model sizes grow, the memory and compute requirements for training these models…
The paper is devoted to studying the performance of a computational pipeline, the number of simultaneously executing stages of which at each time is bounded from above by a fixed number. A look at the restriction as a structural hazard…