Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology
Abstract
The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.
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2D GMM is increasingly recognized as useful for quantifying full 2D shapes of biological and archaeological objects, especially in cranial morphology.
“Although 2D GMM is not a commonly utilized practice among biological anthropologists, its usefulness for quantifying the full 2D shapes of biological and archaeological objects, especially in the study of cranial morphology, is increasingly being recognized [49, 50].”
From Investigating intentional cranial modification: A hybridized two-dimensional/three-dimensional study of the Hirota site, Tanegashima, Japan (2023) · cites this paper as [49]
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A Morphometric Outline Analysis of Ancestry and Sex Differences in Cranial Shape
Murphy, R. E., & Garvin, H. M. (2018) · Journal of Forensic Sciences · doi:10.1111/1556-4029.13699 · Cited by 34 · see citing works
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“Although 2D GMM is not a commonly utilized practice among biological anthropologists, its usefulness for quantifying the full 2D shapes of biological and archaeological objects, especially in the study of cranial morphology, is increasingly being recognized [49, 50].”
Background
- Authors
- Caple, J., Byrd, J., & Stephan, C. N.
- Affiliations
- The University of Queensland (AU)
- Corresponding author
- Caple, Jodi
- Venue
- International Journal of Legal Medicine
- Published
- 2017-02-17
- Volume
- 131
- Issue
- 6
- Pages
- 1675-1690
- ISSN
- 0044-3433 (ISSN-L)
- 0937-9827
- 1437-1596
- OpenAlex
- W2588675660
- Cited by
- 104
- References
- 71
- Citations by year
- 2026: 15 · 2025: 14 · 2024: 12 · 2023: 13 · 2022: 16 · 2021: 11 · 2020: 5 · 2019: 10 · 2018: 5 · 2017: 3
- FWCI
- 10.69
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- International Journal of Legal Medicine (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Social Sciences › Arts and Humanities › Archeology › Forensic Anthropology and Bioarchaeology Studies
- Physical Sciences › Mathematics › Geometry and Topology › Morphological variations and asymmetry
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image Processing and 3D Reconstruction
- Keywords
- elliptic Fourier analysis, skeletal morphology, curve fitting, Fourier harmonics, osteology, forensic anthropology, statistical shape analysis, software tools
- MeSH terms
- Bone and Bones, Fourier Analysis, Humans, Software, Forensic Anthropology, Anatomic Landmarks
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