MATLAB Code Implementation for Circle Fitting

Circle fitting is a common data fitting problem where the objective is to find an optimal circle that minimizes the sum of squared distances from a given set of discrete points to the circle's circumference. In MATLAB, efficient circle fitting can be achieved using geometric approaches and least-squares optimization methods. Key Implementation Steps Data Preprocessing: First, ensure point data is stored in matrix format, such as an N×2 matrix where each row represents the (x, y) coordinates of a point. MATLAB's matrix operations can efficiently handle this structured data. Geometric Center Estimation: An initial circle center can be roughly estimated using the mean of data points, but more accurate methods typically involve least-squares optimization for both center coordinates and radius. Least-Squares Optimization: Transform the problem into an optimization task by minimizing the distance error between all points and the circle. Solve for center coordinates (a, b) and radius r using methods like algebraic fitting (e.g., Kåsa method) or geometric fitting (more precise but computationally intensive). In MATLAB, the `lsqnonlin` function from the Optimization Toolbox can implement nonlinear least-squares optimization effectively. Result Validation: Calculate fitting errors such as Root Mean Square Error (RMSE) to evaluate the quality of the fit. MATLAB's built-in functions like `sqrt(mean(residuals.^2))` can compute RMSE efficiently. Critical Implementation Tips Utilize matrix operations to accelerate computations and avoid loops for better performance. Leverage optimization toolboxes like `lsqnonlin` for nonlinear least-squares optimization. For noisy data, consider robust fitting methods such as RANSAC (Random Sample Consensus) to improve accuracy. Extended Applications Circle fitting has wide engineering applications, including detecting circular contours of mechanical components and analyzing astronomical orbits. MATLAB's Curve Fitting Toolbox provides convenient interfaces for rapid implementation, offering pre-built functions and graphical tools to simplify the fitting process.