Application of nonlinear least squares fitting to parameterized shapes
Description
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.
Files
Steps to reproduce
The original database from which images of the different diatom species were taken was provided by the Royal Botanic Garden Edinburgh and is available at the following link: https://websites.rbge.org.uk/ADIAC/ . Seed images were captured under the following procedure: The image capture system consisted of a white light box, a brightness control, a 6.48 Mpx monochrome camera (Basler aca3088-57um), and a 35 mm prime lens (Edmund Optics Lens CFFL F1. 7 F35mm 2/3"); it was controlled by a laptop computer (i7 core 3.3 GHz processor, 16 GB memory and GTX 1070 graphics card) through the Basler pylon Camera Software Suite avoiding any kind of vibration during image acquisition. The camera was placed in the top view, capturing the seed plane which was scaled using a 1 mm precision ruler. This system made it possible to acquire highly contrasted images with almost no shadows. To reproduce the results, download the codes into MATLAB in a single folder and adapt the paths so that they are able to take the necessary data for making the adjustments.
Institutions
- Universidad Veracruzana