# Optical and SAR Image Registration Based on the Phase Congruency Framework
###### Abstract  
The improved phase congruency (PC) algorithms have been successfully applied to optical and synthetic aperture radar (SAR) image registration since they are insensitive to nonlinear radiometric and geometric differences. However, most of the algorithms are sensitive to large-scale differences and rotation differences between optical and SAR images. To tackle this, we propose a PC framework to register optical and SAR images. It is compatible with large-scale and rotation invariance. Firstly, a multi-scale Harris keypoint extraction method based on the maximum moment of PC (  
was robust to nonlinear intensity transformation, but it was sensitive to geometric and radiometric differences between optical and SAR images. [PERSON] et al. [9] extended the nonlinear diffusion method to extract uniformly distributed keypoints. They proposed a structural descriptor based on the PC information. [PERSON] et al. [10] proposed a SIFT-like algorithm for optical and SAR images (OS-SIFT). It used a multi-scale Harris detector to improve the keypoint repeatability between optical and SAR images. These above algorithms provided the registration framework based on the keypoint-based method. In addition, for the line-based method, [PERSON] et al. [11] proposed the features and spectral graph theory to perform SAR and optical image registration. The algorithm extracted line segments, and defined the intersection points between different line segments as keypoints. However, the algorithm was inapplicable to the situation with little structural information. At present, the most popular keypoint extraction method is to extract corner points from the image composed solely of edge information. In optical and SAR images, the edge features obtained by the PC maximum moment are consistent, so the corner point detection methods based on the PC maximum moment are popular with researchers. [PERSON] et al. [12] used the orientation histogram based on the PC model to deal with the nonlinear radiometric difference between optical and SAR images. It used PC information to reflect the structural properties. However, it was sensitive to scale and geometric differences. [PERSON] et al. [13] proposed a radiation-variation insensitive feature transform method. It replaces the image intensity values with the PC information to extract keypoints, which improves the compatibility with the radiometric difference between optical and SAR image pairs. However, the algorithm does not consider the scale invariance, so it cannot match the optical and SAR images with large-scale differences. [PERSON] et al. [14] used the complexity analysis method to obtain keypoints, and combined the PC maximum moment with the binary mode to build the novel descriptor. Although the porposed algorithm can overcome the geometric and radiometric differences between optical and SAR images, it is only compatible with small-scale and rotation differences. [PERSON] et al. [15] proposed a 3D descriptor based on the oriented gradients, and it improved the robustness of the registration results. However, it cannot solve large-scale and rotation differences. Meanwhile, [PERSON] et al. [16] used the novel nonlinear diffusion scale space to obtain the keypoints, and it improved the computational efficiency by optimizing the number of matching correspondences. For the optical and SAR remote sensing image registration, PC-based algorithms are more robust to nonlinear radiometric and geometric differences. However, most of them are sensitive to scale and rotation differences between optical and SAR images. To solve this problem, we propose an algorithm based on the PC framework, which takes the scale and rotation differences between optical and SAR images into account. The main contributions of the proposed algorithm are as follows:  
1. To solve the problem that the scale invariance is not considered in the PC-based algorithms, we propose a novel multi-scale space based on the PC algorithm, which is constructed by the convolution of the maximum moment map and log-Gabor filter.