The primary requirement for cross-modal data fusion is the precise alignment of data from different sensors. However, the calibration between LiDAR point clouds and camera images is typically time-consuming and needs external calibration board or specific environmental features. Cross-modal registration effectively solves this problem by aligning the data directly without requiring external calibration. However, due to the domain gap between the point cloud and the image, existing methods rarely achieve satisfactory registration accuracy while maintaining real-time performance. To address this issue, we propose a framework that projects point clouds into several 2D representations for matching with camera images, which not only leverages the geometric characteristic of LiDAR point clouds more effectively but also bridge the domain gap between the point cloud and image. Moreover, to tackle the challenges of cross modal differences and the limited overlap between LiDAR point clouds and images in the image matching task, we introduce a multi-scale feature extraction network to effectively extract features from both camera images and the projection maps of LiDAR point cloud. Additionally, we propose a patch-to-pixel matching network to provide more effective supervision and achieve higher accuracy. We validate the performance of our model through experiments on the KITTI and nuScenes datasets. Our network achieves real-time performance and extremely high registration accuracy. On the KITTI dataset, our model achieves a registration accuracy rate of over 99\%.