# Reframing Three-Dimensional Morphometrics Through Functional Data Innovations

## TL;DR

This paper introduces innovative functional data analysis methods, including SRVF and arc-length parameterisation, to enhance 3D morphometric analysis, demonstrated through simulations and classification of kangaroo dietary categories.

## Contribution

It develops seven new pipelines integrating functional data analysis with geometric morphometrics, improving 3D shape analysis by considering curvature and elastic alignment.

## Key findings

- Functional data analysis improves 3D morphometric robustness
- Arc-length and SRVF approaches enhance shape differentiation
- New pipelines outperform standard geometric morphometrics in classification tasks

## Abstract

This study innovates geometric morphometrics by incorporating functional data analysis, the square-root velocity function (SRVF), and arc-length parameterisation for 3D morphometric data, leading to the development of seven new pipelines in addition to the standard geometric morphometrics (GM) approach.. This enables three-dimensional images to be examined from perspectives that do not neglect curvature, through the combined use of arc-length parameterisation, soft-alignment, and elastic-alignment. A simulation study was conducted to demonstrate the general effectiveness of eight pipelines: geometric morphometrics (GM, baseline), arc-GM, functional data morphometrics (FDM), arc-FDM, soft-SRV-FDM, arc-soft-SRV-FDM, elastic-SRV-FDM, and arc-elastic-SRV-FDM. These pipelines were also applied to distinguish dietary categories of kangaroos (omnivores, mixed feeders, browsers, and grazers) using cranial landmarks obtained from 41 extant species. Principal component analysis was conducted, followed by classification analysis using linear discriminant analysis, multinomial regression and support vector machines with a linear kernel. The results highlight the effectiveness of functional data analysis, together with arc-length and SRVF-based approaches, in opening the door to more robust perspectives for analysing three-dimensional morphometrics, while establishing geometric morphometrics as the baseline for comparison.