Circle Center Fitting Using Least Squares Estimation

In computer vision and image processing applications, circles represent fundamental geometric shapes with widespread utility across various domains. Least squares estimation serves as a predominant mathematical approach for circle fitting, enabling precise computation of both center coordinates and radius parameters. The implementation typically involves solving the circle equation (x-a)² + (y-b)² = r² through linearization techniques, where the objective function minimizes the sum of squared residuals between observed points and the fitted circle. This method employs matrix operations to solve the normal equations, often utilizing Singular Value Decomposition (SVD) or QR decomposition for numerical stability. By applying least squares circle fitting, researchers and engineers achieve enhanced measurement accuracy for circular objects, leading to improved outcomes in machine vision systems, automated inspection processes, non-destructive testing methodologies, and medical imaging applications.