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Targetless Lidar-camera registration is a repeating task in many computer vision and robotics applications and requires computing the extrinsic pose of a point cloud with respect to a camera or vice-versa. Existing methods based on learning or optimization lack either generalization capabilities or accuracy. Here, we propose a combination of pre-training and optimization using a neural network-based mutual information estimation technique (MINE [1]). This construction allows back-propagating the gradient to the calibration parameters and enables stochastic gradient descent. To ensure orthogonality constraints with respect to the rotation matrix we incorporate Lie-group techniques. Furthermore, instead of optimizing on entire images, we operate on local patches that are extracted from the temporally synchronized projected Lidar points and camera frames. Our experiments show that this technique not only improves over existing techniques in terms of accuracy, but also shows considerable generalization capabilities towards new Lidar-camera configurations.