Reliable and superior elliptic Fourier descriptor normalization and its application software ElliShape with efficient image processing

TL;DR

This paper introduces a novel, invariant elliptic Fourier descriptor normalization method and the ElliShape software, enhancing shape analysis accuracy, robustness, and efficiency for complex digital images in biological and ecological research.

Contribution

The paper presents a true EFD normalization approach invariant to all basic contour transformations and develops ElliShape, a user-friendly software integrating improved contour extraction and analysis.

Findings

ElliShape outperforms existing tools in shape reconstruction accuracy.

The new normalization method ensures invariance under all basic contour transformations.

ElliShape demonstrates robustness and efficiency in processing complex digital images.

Abstract

Elliptic Fourier analysis (EFA) is a powerful tool for shape analysis, which is often employed in geometric morphometrics. However, the normalization of elliptic Fourier descriptors has persistently posed challenges in obtaining unique results in basic contour transformations, requiring extensive manual alignment. Additionally, contemporary contour/outline extraction methods often struggle to handle complex digital images. Here, we reformulated the procedure of EFDs calculation to improve computational efficiency and introduced a novel approach for EFD normalization, termed true EFD normalization, which remains invariant under all basic contour transformations. These improvements are crucial for processing large sets of contour curves collected from different platforms with varying transformations. Based on these improvements, we developed ElliShape, a user-friendly software. Particularly, the improved contour/outline extraction employs an interactive approach that combines automatic contour generation for efficiency with manual correction for essential modifications and refinements. We evaluated ElliShape's stability, robustness, and ease of use by comparing it with existing software using standard datasets. ElliShape consistently produced reliable reconstructed shapes and normalized EFD values across different contours and transformations, and it demonstrated superior performance in visualization and efficient processing of various digital images for contour analysis.The output annotated images and EFDs could be utilized in deep learning-based data training, thereby advancing artificial intelligence in botany and offering innovative solutions for critical challenges in biodiversity conservation, species classification, ecosystem function assessment, and related critical issues.