Minimizing Geometric Distance by Iterative Linear Optimization

This paper proposes an algorithm that solves planar homography by iterative linear optimization. We iteratively employ direct linear transformation (DLT) algorithm to robustly estimate the homography induced by a given set of point correspondences under perspective transformation. By simple on-the-fly homogeneous coordinate adjustment we progressively minimize the difference between the algebraic error and the geometric error. When the difference is sufficiently close to zero, the geometric error is equivalently minimized and the homography is reliably solved. Backward covariance propagation is employed to do error analysis. The experiments prove that the algorithm is able to find global minimum despite erroneous initialization. It gives very precise estimate at low computational cost and greatly outperforms existing techniques.