# Robust Morphometric Analysis based on Landmarks. Applications

## TL;DR

This paper enhances Procrustes Analysis for morphometric landmark data by introducing robustness to outliers and providing statistical tests for differences, with practical GIS applications.

## Contribution

It introduces a robust version of Procrustes Analysis and derives a new tail probability approximation for the Procrustes Statistic under near-normal conditions.

## Key findings

- Robust classification of individuals using the modified Procrustes method.
- New statistical test for significant differences between individuals.
- Applications demonstrated with GIS tools.

## Abstract

Procrustes Analysis is a Morphometric method based on Configurations of Landmarks that estimates the superimposition parameters by least-squares; for this reason, the procedure is very sensitive to outliers. In the first part of the paper we robustify this technique to classify individuals from a descriptive point of view. In the literature there are also classical results, based on the normality of the observations, to test whether there are significant differences between individuals. In the second part of the paper we determine a Von Mises plus Saddlepoint approximation for the tail probability of the Procrustes Statistic when the observations come from a model close to the normal. We conclude the paper with some applications using the Geographical Information System QGIS.