Mobile Mapping Systems are now commonly used in large urban acquisition campaigns. They are often equiped with LiDAR sensors and optical cameras, providing very large multimodal datasets. The fusion of both modalities serves different purposes such as point cloud colorization, geometry enhancement or object detection. However, this fusion task cannot be done directly as both modalities are only coarsely registered. This paper presents a fully automatic approach for LiDAR projection and optical image registration refinement based on LiDAR point cloud 3D renderings. First, a coarse 3D mesh is generated from the LiDAR point cloud using the sensor topology. Then, the mesh is rendered in the image domain. After that, a variational approach is used to align the rendering with the optical image. This method achieves high quality results while performing in very low computational time. Results on real data demonstrate the efficiency of the model for aligning LiDAR projections and optical images.