A symmetric objective function for ICP

The Iterative Closest Point (ICP) algorithm, commonly used for alignment of 3D models, has previously been defined using either a point-to-point or point-to-plane objective. Alternatively, researchers have proposed computationally-expensive methods that directly minimize the distance function between surfaces. We introduce a new symmetrized objective function that achieves the simplicity and computational efficiency of point-to-plane optimization, while yielding improved convergence speed and a wider convergence basin. In addition, we present a linearization of the objective that is exact in the case of exact correspondences. We experimentally demonstrate the improved speed and convergence basin of the symmetric objective, on both smooth models and challenging cases involving noise and partial overlap.