EigenFactors: Plane Estimation for MultiFrame and TimeContinuous Point Cloud Alignment In this paper, we introduce the EigenFactor (EF) method, which estimates a planar surface from a set of point clouds (PCs), with the peculiarity that these points have been observed from different poses, i.e. the trajectory described by a sensor. We propose to use multiple EigenFactors (EFs) or different planesxe2x80x99 estimations, that allow to solve the multiframe alignment over a sequence of observed PCs. Moreover, the complexity of the EFs optimization is independent of the number of points, but depends on the number of planes and poses. To achieve this, a closedform of the gradient is derived by differentiating over the minimum eigenvalue with respect to poses, hence the name EigenFactor. In addition, a timecontinuous trajectory version of EFs is proposed. The EFs approach is evaluated on a simulated environment and compared with two variants of ICP, showing that it is possible to optimize over all point errors, improving both the accuracy and computational time. Code has been made publicly available.

Joint Registration of Multiple Point Sets with Refinement The recent advances in fast and affordable 3D scanners, such as the Microsoft Kinect, have triggered new developments in 3D reconstruction. However, the geometric alignment of multiple point clouds is still a very challenging task. This paper addresses the problem of registering multiple point sets by building upon the stateoftheart Joint Registration of Multiple Point Clouds (JRMPC) algorithm. We advance over JRMPC by incorporating the surface normal orientation of each point in the Gaussian Mixture Models (GMM) employed by this method. We formally derive an expectationconditional maximization algorithm that iteratively estimates the refined model and transformation parameters. Experiments performed on both synthetic, real indoor and outdoor data prove that incorporating the orientation information substantially improves the parameter estimation, allowing for a 50% average reduction of the registration error compared to JRMPC. Our method is compared to other pairwise approaches, demonstrating the best performance on three different realistic datasets.