Continuous Fields and Discrete Samples: Reconstruction through Delaunay Tessellations

TL;DR

This paper presents the Delaunay Density Estimator Method, a novel adaptive technique for reconstructing continuous density fields from discrete samples, effectively capturing complex anisotropic structures in astronomical data.

Contribution

The paper introduces a new Delaunay tessellation-based method for density field reconstruction that adapts to local data density and preserves anisotropic features.

Findings

Successfully reconstructs high-resolution density in dense regions

Effectively captures anisotropic features like filaments and walls

Reduces shot-noise effects in low-density regions

Abstract

Here we introduce the Delaunay Density Estimator Method. Its purpose is rendering a fully volume-covering reconstruction of a density field from a set of discrete data points sampling this field. Reconstructing density or intensity fields from a set of irregularly sampled data is a recurring key issue in operations on astronomical data sets, both in an observational context as well as in the context of numerical simulations. Our technique is based upon the stochastic geometric concept of the Delaunay tessellation generated by the point set. We shortly describe the method, and illustrate its virtues by means of an application to an N-body simulation of cosmic structure formation. The presented technique is a fully adaptive method: automatically it probes high density regions at maximum possible resolution, while low density regions are recovered as moderately varying regions devoid of the often irritating shot-noise effects. Of equal importance is its capability to sharply and undilutedly recover anisotropic density features like filaments and walls. The prominence of such features at a range of resolution levels within a hierarchical clustering scenario as the example of the standard CDM scenario is shown to be impressively recovered by our scheme.