Levenberg-Marquardt Optimization for Homography Matrix

The Levenberg-Marquardt optimization algorithm is a widely-used nonlinear least-squares method, commonly implemented in computer vision libraries like OpenCV or MATLAB. It effectively refines homography matrices by iteratively adjusting parameters to minimize reprojection errors between corresponding points. The algorithm dynamically blends gradient descent and Gauss-Newton approaches using a damping parameter λ - increasing λ for stability in steep regions and decreasing it for faster convergence near minima. For camera calibration, it optimizes intrinsic/extrinsic parameters by minimizing the difference between observed and projected 3D-2D point pairs. Implementation typically involves computing Jacobian matrices for partial derivatives and performing matrix inversion via singular value decomposition (SVD). This hybrid optimization strategy ensures robust convergence, making it particularly valuable for enhancing the accuracy and stability of calibration results in computer vision applications.