Elliptic Fourier analysis (EFA) is often employed in geometric morphometrics (GM), but the normalization of elliptic Fourier descriptor (EFD) has persistently posed challenges for obtaining unique and comparable results, especially in the application of outline-based GM methods, which limits the implementation in automated analysis of numerous, highly variable and multi-dimensional biological forms.

In this paper, we introduce an approach for complete elliptic Fourier descriptor (EFD) normalization, which remains constant under all basic contour transformations with theoretical derivations. Accordingly, we propose to use minimum Euclidean distance between two shapes reconstructed by completely normalized EFDs for quantitative morphological comparisons, which is mathematically guaranteed to obtain unique and comparable results.

The proposed complete EFD normalization procedure is validated using a benchmark dataset. Using the proposed quantitative morphological analysis, we compared 1338 leaf shapes from 86 species and constructed a morphological tree. The resulting tree shows clustering patterns linked to variations in leaf ellipticity and lobation.

The completely normalized EFDs and corresponding contours can be further utilized in deep learning-based data training for accurate shape identification. Moreover, the integration of geometric morphometrics and machine learning is very useful for integrative taxonomy, biodiversity conservation, species classification and ecosystem function assessment, thereby promoting cross-scale biological research driven by morphological big data.