MATLAB Code Implementation for Ellipse Fitting

The following MATLAB code implements an algorithm for ellipse fitting using the least squares method. Our implementation processes input data containing a minimum of 5 points to generate an optimal ellipse fit through mathematical optimization. The algorithm employs algebraic distance minimization to solve the conic equation Ax² + Bxy + Cy² + Dx + Ey + F = 0, ensuring proper ellipse constraints are maintained during parameter estimation. This implementation is particularly valuable for analyzing elliptical characteristics and pattern recognition applications. Key functions include data normalization for numerical stability, constraint handling to prevent degenerate solutions, and error computation for fit quality assessment. The code structure features modular components for data preprocessing, matrix formulation using scatter matrices, eigenvalue decomposition for parameter extraction, and geometric transformation to obtain standard ellipse parameters (center coordinates, semi-axes lengths, and rotation angle). The algorithm finds practical applications in image processing pipelines for object detection and computer vision systems for shape recognition tasks. For professionals working in these domains, understanding this implementation's mathematical foundation and optimization approach can significantly enhance geometric analysis capabilities and improve task performance in elliptical feature extraction scenarios.