Application of nonlinear least squares fitting to parameterized shapes

This work presents the ParamFit algorithm, which proposes a parametric function for fitting simple closed curves and a methodology for determining the initial conditions for the Levenberg-Marquardt fitting algorithm. The parametric function is evaluated in three different applications: images of seeds, diatoms, and some well-known geometric planar curves. Furthermore, it is compared with the neural network model (PointNet). The fitting validation was performed using the Jaccard metric, the coefficient of determination (R^2), the mean square error, (RMSE) and the residual error. The results obtained show that the newly proposed parametric function provides high levels of precision, particularly excelling in the classification of seeds and diatoms, with potential applications in agriculture and ecology for the selection and monitoring of species.