Related papers: Exact computation of the halfspace depth

In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…

This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a high-order immersed boundary technique that computes on a…

Tukey depth regions are important notions in nonparametric multivariate data analysis. A $\tau$-th Tukey depth region $\mathcal{D}_{\tau}$ is the set of all points that have at least depth $\tau$. While the Tukey depth regions are easily…

Accuracy and Availability computations for a GNSS System - or combination of Systems - through Service Volume Simulations take considerable time. Therefore, the computation of the accuracy in 2D and 3D are often simplified by an approximate…

For given depth of a we derive a formula for the depth of the image of that term under a given hypersubstitution.

Running time of the light field depth estimation algorithms is typically high. This assessment is based on the computational complexity of existing methods and the large amounts of data involved. The aim of our work is to develop a simple…

We present an algorithm which computes the Hilbert depth of a graded module based on a theorem of Uliczka. Connected to a Herzog's question we see that the Hilbert depth of a direct sum of modules can be strictly bigger than the Hilbert…

An exact algorithm is presented for solving edge weighted graph partitioning problems. The algorithm is based on a branch and bound method applied to a continuous quadratic programming formulation of the problem. Lower bounds are obtained…

Clustering is one of the major tasks in data mining. In the last few years, Clustering of spatial data has received a lot of research attention. Spatial databases are components of many advanced information systems like geographic…

We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…

Data depth is a well-known and useful nonparametric tool for analyzing functional data. It provides a novel way of ranking a sample of curves from the center outwards and defining robust statistics, such as the median or trimmed means. It…

This paper presents a point cloud downsampling algorithm for fast and accurate trajectory optimization based on global registration error minimization. The proposed algorithm selects a weighted subset of residuals of the input point cloud…

The continual improvement of 3D sensors has driven the development of algorithms to perform point cloud analysis. In fact, techniques for point cloud classification and segmentation have in recent years achieved incredible performance…

In this paper, we explore point-cloud based deep learning models to analyze numerical simulations arising from finite element analysis. The objective is to classify automatically the results of the simulations without tedious human…

We provide two algorithms for computing the volume of a convex polytope with half-space representation {x>=0; Ax <=b} for some (m,n) matrix A and some m-vector b. Both algorithms have a O(n^m) computational complexity which makes them…

We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflection seismology. In both algorithms, the main idea is to…

Similar to algorithms, which consume time and memory to run, hardware requires resources to function. For devices processing physical waves, implementing operations needs sufficient "space," as dictated by wave physics. How much space is…

Subspace clustering algorithms are notorious for their scalability issues because building and processing large affinity matrices are demanding. In this paper, we introduce a method that simultaneously learns an embedding space along…

This paper presents a neural network to estimate a detailed depth map of the foreground human in a single RGB image. The result captures geometry details such as cloth wrinkles, which are important in visualization applications. To achieve…

Numerous point-cloud understanding techniques focus on whole entities and have succeeded in obtaining satisfactory results and limited sparsity tolerance. However, these methods are generally sensitive to incomplete point clouds that are…