MATLAB Implementation of Least Squares Method for Ellipse Detection and Fitting

The least squares method can automatically detect and fit ellipses in images. Its principle is based on image fitting algorithms in image processing technology, where the algorithm analyzes and processes data points in the image to derive the fitted ellipse. The least squares method is a mathematical optimization technique that minimizes the error of data points to achieve optimal fitting results. In ellipse detection applications, this method can accurately fit all ellipses present in images and can be applied to various image types, such as natural scenes, industrial products, and medical images. The implementation typically involves extracting edge points using image processing techniques like Canny edge detection, then applying least squares fitting to the elliptical equation Ax² + Bxy + Cy² + Dx + Ey + F = 0. Key MATLAB functions involved may include edge detection functions, matrix operations for solving linear equations (using the backslash operator or pinv function), and optimization techniques for parameter estimation. Therefore, using the least squares method for ellipse detection is a highly effective approach that can significantly improve the accuracy and reliability of image processing tasks. The method's robustness makes it suitable for handling noisy data and partial elliptical arcs commonly encountered in real-world images.