A Direct Least Squares-Based Ellipse Fitting Algorithm Implementation in MATLAB

This article presents a novel direct ellipse fitting algorithm based on least squares method implemented in MATLAB. The algorithm features a direct computational approach that bypasses intermediate parameter conversions, resulting in improved numerical stability and reduced computational complexity. The implementation utilizes MATLAB's matrix operations and linear algebra capabilities to solve the constrained least squares problem efficiently. We provide the complete source code for this algorithm, which includes key functions for data preprocessing, constraint matrix formulation, and eigenvalue decomposition for ellipse parameter extraction. The code demonstrates practical implementation of algebraic distance minimization while maintaining the elliptical constraint through proper scaling and normalization techniques. The algorithm's advantages include robust performance with noisy data, mathematical simplicity, and computational efficiency suitable for real-time applications. We discuss its optimal application scenarios, including computer vision systems, quality control in manufacturing, and biomedical image analysis. The implementation handles both complete and partial elliptical data points through adaptive weighting mechanisms. This resource offers valuable insights for researchers and practitioners working on curve fitting problems, pattern recognition, and image processing applications, providing both theoretical understanding and practical implementation guidance for ellipse fitting challenges.