  Point cloud registration sits at the core of many important and challenging
3D perception problems including autonomous navigation, SLAM, object/scene
recognition, and augmented reality. In this paper, we present a new
registration algorithm that is able to achieve state-of-the-art speed and
accuracy through its use of a hierarchical Gaussian Mixture Model (GMM)
representation. Our method constructs a top-down multi-scale representation of
point cloud data by recursively running many small-scale data likelihood
segmentations in parallel on a GPU. We leverage the resulting representation
using a novel PCA-based optimization criterion that adaptively finds the best
scale to perform data association between spatial subsets of point cloud data.
Compared to previous Iterative Closest Point and GMM-based techniques, our
tree-based point association algorithm performs data association in
logarithmic-time while dynamically adjusting the level of detail to best match
the complexity and spatial distribution characteristics of local scene
geometry. In addition, unlike other GMM methods that restrict covariances to be
isotropic, our new PCA-based optimization criterion well-approximates the true
MLE solution even when fully anisotropic Gaussian covariances are used.
Efficient data association, multi-scale adaptability, and a robust MLE
approximation produce an algorithm that is up to an order of magnitude both
faster and more accurate than current state-of-the-art on a wide variety of 3D
datasets captured from LiDAR to structured light.
