Related papers: Adaptive Binning of X-ray data with Weighted Voron…
We review the concepts of the Voronoi binning technique (Cappellari & Copin 2003), which optimally solves the problem of preserving the maximum spatial resolution of general two-dimensional data, given a constraint on the minimum…
We present new techniques to perform adaptive spatial binning of two-dimensional (2D) data to reach a chosen constant signal-to-noise ratio per bin. These methods are required particularly for the proper analysis of Integral Field…
We present a simple method for adaptively binning the pixels in an image. The algorithm groups pixels into bins of size such that the fractional error on the photon count in a bin is less than or equal to a threshold value, and the size of…
Adaptive binning is a crucial step in the analysis of large astronomical datasets, such as those from integral-field spectroscopy, to ensure a sufficient signal-to-noise ratio (S/N) for reliable model fitting. However, the widely used…
We present new techniques to perform adaptive spatial binning of Integral-Field Spectroscopic (IFS) data to reach a chosen constant signal-to-noise ratio per bin. These methods are required for the proper analysis of IFS observations, but…
We present a new technique for choosing spatial regions for X-ray spectroscopy, called "contour binning". The method chooses regions by following contours on a smoothed image of the object. In addition we re-explore a simple method for…
The Voronoi Density Estimator (VDE) is an established density estimation technique that adapts to the local geometry of data. However, its applicability has been so far limited to problems in two and three dimensions. This is because…
The Voronoi tessellation is a natural way of space segmentation, which has many applications in various fields of science and technology, as well as in social sciences and visual art. The varieties of the Voronoi tessellation methods are…
For the analysis of systems consisting of small, regular objects, the methods of mathematical morphology applied to images of these systems are well-suited. One of these methods is the use of Voronoi polygons. It was found that the Voronoi…
We have developed a novel method of determining 2D radial density profiles for astronomical systems of discrete objects using Voronoi tessellations. This Voronoi-based method was tested against the standard annulus-based method on 5…
Color image segmentation is a crucial step in many computer vision and pattern recognition applications. This article introduces an adaptive and unsupervised clustering approach based on Voronoi regions, which can be applied to solve the…
Conformal prediction constructs a set of labels instead of a single point prediction, while providing a probabilistic coverage guarantee. Beyond the coverage guarantee, adaptiveness to example difficulty is an important property. It means…
In this work, image analysis techniques used in astrophysics to detect low-contrast signals have been adapted in the processing of Computed Tomography (CT) images, combining Centroidal Voronoi Tessellation (CVT) and machine learning…
Given a countable set of points in a continuous space, Voronoi tessellation is an intuitive way of partitioning the space according to the distance to the individual points. As a powerful approach to obtain structural information, it has a…
Probabilistic circuits (PCs) enable exact and tractable inference but employ data independent mixture weights that limit their ability to capture local geometry of the data manifold. We propose Voronoi tessellations (VT) as a natural way to…
We use a sample of 350 star-forming galaxies at $1.25<z<2.66$ from the MOSFIRE Deep Evolution Field survey to demonstrate an improved Voronoi binning technique that we use to study the properties of resolved stellar populations in $z\sim2$…
A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in {\it ab-initio} electronic-structure calculations. We combine a weighted Voronoi tessellation with…
Despite the success of various methods in addressing the issue of spatial reconstruction of dynamical systems with sparse observations, spatio-temporal prediction for sparse fields remains a challenge. Existing Kriging-based frameworks for…
We introduce graph wedgelets - a tool for data compression on graphs based on the representation of signals by piecewise constant functions on adaptively generated binary graph partitionings. The adaptivity of the partitionings, a key…
In this paper we make an attempt to combine the two kinds of data from the Swift-XRT instrument (windowed timing and photon counting modes) and the from BAT. A thorough desription of the applied procedure will be given. We apply various…