Ellipse Fitting for Discrete Data Using Least Squares Method

This documentation presents a comprehensive study on applying the least squares method to discrete data for ellipse fitting. The author successfully implements an algorithm that minimizes the sum of squared residuals between the observed data points and the fitted elliptical model. The implementation typically involves solving a system of linear equations derived from the general quadratic curve equation Ax² + Bxy + Cy² + Dx + Ey + F = 0 with ellipse-specific constraints (B² - 4AC < 0). Key computational steps include matrix operations for parameter estimation and constraint enforcement to ensure valid elliptical solutions. Despite requiring significant computational effort and careful parameter tuning, the final results demonstrate accurate fitting performance with minimized error metrics. The author has chosen to share this validated implementation to provide researchers with a reliable tool for geometric pattern recognition and curve fitting applications, complete with proper error handling and convergence checks.