We propose an algorithm for automatic, targetless, extrinsic calibration of a LiDAR and camera system using semantic information. We achieve this goal by maximizing mutual information (MI) of semantic information between sensors, leveraging a neural network to estimate semantic mutual information, and matrix exponential for calibration computation. Using kernel-based sampling to sample data from camera measurement based on LiDAR projected points, we formulate the problem as a novel differentiable objective function which supports the use of gradient-based optimization methods. We also introduce an initial calibration method using 2D MI-based image registration. Finally, we demonstrate the robustness of our method and quantitatively analyze the accuracy on a synthetic dataset and also evaluate our algorithm qualitatively on KITTI360 and RELLIS-3D benchmark datasets, showing improvement over recent comparable approaches.
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