Direct Least Squares Ellipse Fitting

In image processing applications, ellipse fitting represents a significant computational challenge. The direct least squares method serves as a popular ellipse fitting approach due to its simplicity and computational efficiency. This program proves particularly suitable for beginners starting ellipse fitting research, as it employs clear mathematical principles and straightforward implementation. The core algorithm works by minimizing the algebraic distance between data points and a general conic section, with a constraint matrix ensuring the solution represents a valid ellipse rather than other conic sections. The implementation typically involves constructing a scatter matrix from coordinate data, solving a generalized eigenvalue problem, and extracting parameters from the eigenvector corresponding to the smallest positive eigenvalue. Users can easily modify and customize the code to accommodate broader application scenarios, such as adding robustness to outliers through weighting schemes or extending to 3D ellipse fitting. In summary, this direct least squares-based ellipse fitting program serves as a practical tool that effectively addresses common computer vision problems while providing an accessible foundation for algorithm development.