A Fourier-invariant method for locating point-masses and computing their attributes

TL;DR

This paper introduces a Fourier-invariant Hermite moment-based method for accurately locating and analyzing point-masses in multi-dimensional data, with applications in biology and astronomy.

Contribution

It presents a novel, rigorous approach leveraging Fourier-invariant Hermite moments for counting, locating, and attribute computation of point-masses in any dimension.

Findings

Effective in processing spatial and Fourier data

Applicable to biological and astronomical data

Provides accurate point-mass localization and attribute analysis

Abstract

Motivated by the interest of observing the growth of cancer cells among normal living cells and exploring how galaxies and stars are truly formed, the objective of this paper is to introduce a rigorous and effective method for counting point-masses, determining their spatial locations, and computing their attributes. Based on computation of Hermite moments that are Fourier-invariant, our approach facilitates the processing of both spatial and Fourier data in any dimension.