# A Fast, Accurate, and Separable Method for Fitting a Gaussian Function

## TL;DR

This paper presents a novel, fast, and accurate method for fitting Gaussian functions to data, leveraging a mathematical trick to simplify parameter estimation and improve computational efficiency.

## Contribution

The paper introduces a new separable algorithm for Gaussian fitting that simplifies parameter estimation using a mathematical trick based on area calculations.

## Key findings

- The method achieves high accuracy in parameter estimation.
- It significantly reduces computation time compared to existing methods.
- The approach is applicable across various scientific disciplines.

## Abstract

The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be used to model an approximation of the Airy disk in image processing, laser heat source in laser transmission welding [1], practical microscopic applications [2], and fluorescence dispersion in flow cytometric DNA histograms [3]. In applied sciences, the noise that corrupts the signal can be modeled by the Gaussian distribution according to the central limit theorem. Thus, by fitting the GF, the corresponding process/phenomena behavior can be well interpreted. This article introduces a novel fast, accurate, and separable algorithm for estimating the GF parameters to fit observed data points. A simple mathematical trick can be used to calculate the area under the GF in two different ways. Then, by equating these two areas, the GF parameters can be easily obtained from the observed data.