## 2 Proposed Method
### Main Direction Calculation and Descriptor Construction  
In SIFT and its improved algorithm, specifying the main direction for the feature point can make it a rotation invariant, and the calculation of the main direction and the construction of the descriptor are all through the feature points in the differential pyramid space image to count the gradient histogram of the neighborhood. The image is obtained, so the gradient direction between the SAR and optical images should be consistent. However, as for the registration of multi-sensor images, due to the huge difference in radiation characteristics between each other, for example, the gradient direction of the matching area are often different. In order to avoid this problem, which may cause registration failure, in this paper, the gradient calculation method based on phase consistency is used to extract the consistent gradient features of SAR and optical images, and we use this basic feature to calculate the main direction of feature points by means of statistical histograms and build descriptors.  
In this section, when calculating the main directions of feature points, we choose the method that approximates the original SIFT algorithm. After the precise coordinates of the feature points and the corresponding scale coordinates are obtained through the detection algorithm, the consistent gradient algorithm is used to calculate the neighboring neighbors of the feature points from the corresponding scale space. In the gradient direction histogram of the domain, the direction corresponding to the maximum peak value is selected as the main direction of the feature point, and the direction with the peak value in the histogram greater than 80% of the main direction peak value is used as the auxiliary direction to improve the stability of the algorithm.  
When constructing the feature point descriptor, this paper makes some modifications to the selection and division of the neighborhood block of the SIFT feature point. The SIFT native structure description method divides the pixels in the radius neighborhood around the feature points into 4+4 sub-blocks in space, and counts the gradient direction histograms of eight directions in each sub-block, and finally divides the directions of all sub-regions into 4+4 sub-blocks. The gradient information combination is a 128-dimensional descriptor. According to the research of [PERSON] et al. this division method ignores the positional relationship between the pixels within the neighborhood block. Therefore, this article adopts the method that selects the image within a certain radius around the feature point as its neighborhood block. After rotating the neighborhood block to the main direction, the pixels in the neighborhood block are divided in the polar coordinate system according to their distance from the center point into different fan-shaped grids, so that 17 grid areas are obtained. For each fan-shaped sub-region and each pixel in the center circle, use the corresponding gradient algorithm to calculate the gradient magnitude and direction, and then assign the gradient value in the sub-block to eight directions, and finally after the gradient information of each direction in the 17 sub-regions is concatenated and normalized, 136 dimensions are obtained, so that the descriptors obtained have better robustness and uniqueness.