Application of nonlinear least squares fitting to parameterized shapes

This paper presents a contour fitting model based on a simple closed parameterisation, designed to capture complex shapes in images without the need for large volumes of training data. The proposed approach was applied and evaluated on three specific domains: seed morphological properties, diatom morphology and geometric plane curves, using metrics such as the coefficient of determination, Jaccard index and root mean square error (RMSE) to validate the accuracy of the fit. The results show that the model provides high levels of accuracy in all applications, with particular strengths in seed and diatom classification, with potential applications in agriculture and ecology for species selection and monitoring. Compared to neural network-based fitting methods, the approach presented here is shown to be a resource-efficient alternative, requiring no lengthy training and achieving significant adaptability to diverse morphologies. These findings suggest that the proposed closed parameterisation is a robust and versatile tool for contour analysis in multiple areas, with potential for extension to other scientific and technical applications.

本文提出了一种基于简单封闭参数化的轮廓拟合模型，旨在无需大量训练数据即可捕捉图像中的复杂形状。该研究方法被应用于三个特定领域：种子形态特征、硅藻形态以及几何平面曲线，并利用决定系数、Jaccard 指数和均方根误差（RMSE）等指标来验证拟合的准确性。研究结果表明，该模型在所有应用中均展现出高度的准确性，尤其在种子和硅藻分类方面表现出显著优势，并具有在农业和生态学领域应用于物种选择和监测的潜力。与基于神经网络的拟合方法相比，本文提出的方法证明是一种资源高效的替代方案，无需长时间的训练，且能够显著适应多样的形态。这些发现表明，所提出的封闭参数化是一种稳健而多功能的轮廓分析工具，具有拓展至其他科学和技术应用领域的潜力。