# An unbiased estimator for the ellipticity from image moments

## TL;DR

This paper introduces a statistically unbiased estimator for the ellipticity of objects in noisy images, based on image moments, assuming Gaussian noise and known point-spread function, improving accuracy in shape measurement.

## Contribution

The paper presents a novel unbiased estimator for ellipticity derived from image moments, accounting for noise and PSF, with an explicit covariance estimate.

## Key findings

- Estimator is unbiased under specified assumptions
- Covariance of the estimator can be explicitly computed
- Method improves shape measurement accuracy in noisy images

## Abstract

An unbiased estimator for the ellipticity of an object in a noisy image is given in terms of the image moments. Three assumptions are made: i) the pixel noise is normally distributed, although with arbitrary covariance matrix, ii) the image moments are taken about a fixed centre, and iii) the point-spread function is known. The relevant combinations of image moments are then jointly normal and their covariance matrix can be computed. A particular estimator for the ratio of the means of jointly normal variates is constructed and used to provide the unbiased estimator for the ellipticity. Furthermore, an unbiased estimate of the covariance of the new estimator is also given.