A Novel Image Registration Method Based on Phase Correlation Using Low-Rank Matrix Factorization With Mixture of Gaussian

Image registration is a critical process for the various applications in the remote sensing community, and its accuracy greatly affects the results of the subsequent applications. Image registration based on phase correlation has been widely concerned due to its robustness to gray differences and efficiency. After calculating the normalized cross-relation matrix Q, the most commonly used approach is fitting the 2-D phase plane that passes through the origin, but it needs to remove contaminated spectrum carefully and the corresponding parameters are empirical. In fact, the phase correlation matrix is rank one for a noise-free translation model. This property simplifies the matching problem to finding the best rank-one approximation of the normalized cross-relation matrix. We develop a novel algorithm that performs the rank-one matrix factorization on the phase correlation matrix by assuming its noise as mixture of Gaussian (MoG) distributions. The MoG model is a general approximator for any continuous distribution, and hence is able to model a wide range of noise distribution. The parameters of the MoG model can be evaluated under the framework of maximum likelihood estimation by using an expectation-maximization method, and the subspace is calculated with standard methods. The advantages of the algorithm, high accuracy, and robustness to aliasing, noise, gray difference, and occlusions are illustrated by a series of simulated and real-image experiments.