Direct Least Squares-Based Ellipse Fitting Algorithm Source Code

This article provides a detailed explanation of a MATLAB-implemented direct ellipse fitting algorithm based on the least squares method. The algorithm employs a mathematical approach that minimizes the algebraic distance between data points and the ellipse model, ensuring higher accuracy in ellipse fitting for various applications. We will discuss key algorithmic concepts including the constraint matrix formulation, eigenvalue decomposition for parameter estimation, and the normalization process that prevents degenerate solutions. The implementation features robust handling of scattered data points through coordinate normalization and includes error-checking mechanisms for invalid configurations. The complete source code is provided with detailed comments explaining each functional segment: the data preprocessing module handles outlier detection, the core fitting function implements the direct least squares solution using matrix operations, and the visualization component generates plots with confidence intervals. This allows researchers to directly integrate the algorithm into their projects while understanding the mathematical foundation behind the elliptical parameter calculation.