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We propose an automatic, targetless, data-driven, extrinsic calibration method to calibrate push-broom 2D lidars with a multi-camera system. The calibration problem is decoupled into alternating optimisers over two hierarchical levels, where both levels are linked with a penalty term. The lower-level optimises the six degrees-of-freedom (DoF) rigidbody transforms between the lidar and each camera of the multi-camera unit by minimising the Normalised Information Distance between intensity measurements obtained from both sensor modalities. The upper-level minimises a nonlinear least squares error between the lower-level solutions. We describe the theory, implement the method, and provide a detailed performance analysis with experiments on real-world data.

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