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The problems of point-cloud registration and attitude estimation from vectorobservations (Wahba's problem) have widespread applications in computer visionand mobile robotics. This work introduces a simple approach for integratingsets of geometric feature observations (points, lines, and planes) in such away that any solution to either point-cloud registration or to Wahba's problemcan be used to find the SE(3) transformation between the two sets thatminimizes the corresponding cost function. We compare the performance of threesolutions: classic Horn's optimal quaternion method, Optimal Linear AttitudeEstimator (OLAE) that efficiently recovers the optimal Gibbs-Rodrigues vectorsolving a small linear system, and an iterative non-linear Gauss-Newton solver.Special care is given to explain how to overcome the Gibbs vector singularityfor OLAE by using the method of sequential rotations. Gross outliers inpoint-to-point correspondences can be discarded by means of detectingtransformation scale mismatches. The approach also allows the introduction ofper-primitive relative weights, including an optional robust loss function thatis applicable only if an initial guess for the solution is known in advance.Experiments are presented to evaluate how the three solutions tolerate noise inthe input data for different kinds of geometric primitives. Finally,experiments with real datasets validate the suitability of the optimalalignment algorithm as the core of an Iterative Closest Point/Primitive (ICP)algorithm. An open-source implementation of all the described algorithms isprovided in https://github.com/MOLAorg/mp2p_icp

OLAE-ICP: Robust and fast alignment of geometric features with the optimal linear attitude estimator