Iterative closest point problem: A tensorial approach to finding the initial guess

Abstract

The iterative closest point (ICP) problem is very important in multiple fields such as robotics, machine vision, automotive or assistive technologies. The problem is to find the optimal transformation that can align two sets of 3D points. Even if in the recent year new variations of ICP were proposed, the algorithm may get trapped in local minima due to the non-convexity of the problem. This issue may be overcome if the initial guess is chosen as close as possible to the true solution. In this paper a tensorial based method is proposed for choosing the initial guess of the iterative closest point problem. This new approach is strongly connected with the parameters that can be used to describe the displacement of rigid bodies. Using an isomorphism between the special Euclidean group SE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> and the orthogonal dual tensors group SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , a detailed procedure is described on how to compute the initial guess for the iterative closest point problem. An evaluation of the proposed method is done using a Matlab framework that implements the ICP algorithm.