# Comparing Samples from the $\mathcal{G}^0$ Distribution using a Geodesic Distance

## TL;DR

This paper introduces a novel method for comparing SAR image samples modeled by the $ ext{G}^0$ distribution using a Geodesic Distance, enabling effective quantification of local texture and scale differences.

## Contribution

It proposes a new approach employing Geodesic Distance for sample comparison from the $ ext{G}^0$ distribution, including three tests and permutation-based distribution estimation.

## Key findings

- Effective discrimination between SAR image samples based on local parameters.
- Three new tests for sample comparison using GD are proposed.
- Permutation methods accurately estimate test probability distributions.

## Abstract

The $\mathcal{G}^0$ distribution is widely used for monopolarized SAR image modeling because it can characterize regions with different degree of texture accurately. It is indexed by three parameters: the number of looks (which can be estimated for the whole image), a scale parameter and a texture parameter. This paper presents a new proposal for comparing samples from the $\mathcal{G}^0$ distribution using a Geodesic Distance (GD) as a measure of dissimilarity between models. The objective is quantifying the difference between pairs of samples from SAR data using both local parameters (scale and texture) of the $\mathcal{G}^0$ distribution. We propose three tests based on the GD which combine the tests presented in~\cite{GeodesicDistanceGI0JSTARS}, and we estimate their probability distributions using permutation methods.