This study presents a generalised least squares based method for fitting polygons and ellipses to data points. The method is based on a trigonometric fitness function that approximates a unit shape accurately, making it applicable to various geometric shapes with minimal fitting parameters. Furthermore, the proposed method does not require any constraints and can handle incomplete data. The method is validated on synthetic and real-world data sets and compared with the existing methods in the literature for polygon and ellipse fitting. The test results show that the method achieves high accuracy and outperforms the referenced methods in terms of root-mean-square error, especially for noise-free data. The proposed method is a powerful tool for shape fitting in computer vision and geometry processing applications.

翻译：本研究提出一种基于广义最小二乘法的多边形与椭圆数据点拟合方法。该方法采用能精确逼近单位形状的三角函数适应度函数，从而以最少拟合参数适用于多种几何形状的拟合。此外，所提方法无需任何约束条件，并能够处理不完整数据。通过在合成数据集与真实世界数据集上的验证，并与现有文献中的多边形及椭圆拟合方法进行对比，测试结果表明：该方法具有高精度，尤其在无噪声数据场景下，其均方根误差显著优于参考文献中的方法。本方法为计算机视觉与几何处理应用中的形状拟合提供了强有力的工具。