We propose a new method for extrinsic calibration of a line-scan LIDAR with a perspective projection camera. Our method is a closed-form, minimal solution to the problem. The solution is a symbolic template found via variable elimination and the multi-polynomial Macaulay resultant. It does not require initialization, and can be used in an automatic calibration setting when paired with RANSAC and least-squares refinement. We show the efficacy of our approach through a set of simulations and a real calibration.

We propose a novel technique for the registration of 3D point clouds which makes very few assumptions: we avoid any manual rough alignment or the use of landmarks, displacement can be arbitrarily large, and the two point sets can have very little overlap. Crude alignment is achieved by estimation of the 3D-rotation from two Extended Gaussian Images even when the data sets inducing them have partial overlap. The technique is based on the correlation of the two EGIs in the Fourier domain and makes use of the spherical and rotational harmonic transforms. For pairs with low overlap which fail a critical verification step, the rotational alignment can be obtained by the alignment of constellation images generated from the EGIs. Rotationally aligned sets are matched by correlation using the Fourier transform of volumetric functions. A fine alignment is acquired in the final step by running Iterative Closest Points with just few iterations.