Detecting structured sources in noisy images via Minkowski maps

TL;DR

This paper introduces a morphometric analysis method using Minkowski maps to detect faint structured sources in noisy images, significantly improving sensitivity and rejection rates without prior source knowledge.

Contribution

The paper presents a novel shape-based analysis technique that enhances detection sensitivity in noisy spatial data by accurately modeling background noise distributions.

Findings

Sensitivity increased by 14 orders of magnitude.

Rejection rates improved by an order of magnitude.

Successfully applied to H.E.S.S. data for faint source detection.

Abstract

Astronomy, biophysics, and material science often depend on the possibility to extract information out of faint spatial signals. Here we present a morphometric analysis technique to quantify the shape of structural deviations in greyscale images. It identifies important features in noisy spatial data, especially for short observation times and low statistics. Without assuming any prior knowledge about potential sources, the additional shape information can increase the sensitivity by 14 orders of magnitude compared to previous methods. Rejection rates can increase by an order of magnitude. As a key ingredient to such a dramatic increase, we accurately describe the distribution of the homogeneous background noise in terms of the density of states $\Omega(A,P,\chi)$ for the area $A$, perimeter $P$, and Euler characteristic $\chi$ of random black-and-white images. The technique is successfully applied to data of the H.E.S.S. experiment for the detection of faint extended sources.