## 1 Introduction
However, in practice, there is parallax between the images to be registered, and the relationship between such kinds of images is often not exact homography transformation. In image registration, it is necessary to estimate the homography matrix between the target image and the reference image. The homography matrix is used to transform the target image to achieve the alignment of the target image and the reference image in spatial coordinates. The transformation process is called image mapping or image transformation. According to the application scope of the homography matrix, image transformation can be divided into global homography transformation and local homography transformation. Global homography transformation [7; 11; 12; 14; 16] uses the same homography matrix to transform the whole image. It requires that the target image and the reference image contain basically the same image information in the overlapping region. It is only suitable for images with small or no parallax. When this condition is not satisfied, the accuracy of image registration will be reduced significantly. Local homography transformation algorithm [17; 18; 19] maps different regions of an image using different transformation matrices, which can better overcome the shortcomings of the global homography transformation algorithm. As-Projective-As-Possible (APAP) algorithm [19] is a representative local homography transformation algorithm. It first extracts the feature matching points between the images and then divides the images into a uniform grid. Moving direct linear transform (MDLT) is used to estimate the homography matrix of each grid. Finally, the homography matrix of each grid is used to implement local homography transformation on the image to be registered. For images that do not satisfy the condition of global homography transformation, the image registration accuracy achieved by APAP algorithm is higher than that achieved by the global homography transformation algorithm [20]. APAP algorithm is also a feature-based image registration algorithm in essence. It also has the characteristics of a feature-based image registration algorithm and has higher accuracy than the general feature-based image registration algorithm. The general image registration algorithm based on global homography transformation only uses one homography matrix estimation and one homography transformation, while APAP algorithm needs multiple homography matrix estimations and homography transformations, so the speed of the APAP algorithm is slower than that of the general feature-based image registration algorithm. The above two deep learning-based image registration algorithms are both for global homography transformation, and the used samples cannot be adopted to estimate the local homography matrix. Therefore, based on the above researches, an image registration algorithm based on deep learning and local homography transformation is proposed in this paper. An image sample and label generation method suitable for local homography transformation is designed so as to train the image registration model with convolutional neural network (CNN) effectively. The resulted image registration model can effectively reduce the error of image registration and overcome the defects of poor robustness of traditional image registration algorithms and low accuracy of existing deep learning-based image registration algorithms. The main contributions of this paper are as follows: (1) A CNN and local homography transformation-based algorithm are proposed to solve the problem of image registration, which is a useful exploration for deep learning to solve the problem of image registration; (2) an image sample and label generation method suitable for local homography transformation is proposed, and the generated samples have good diversity and can simulate the actual image registration situation. The rest of this paper is organized as follows.