  Registering accurately point clouds from a cheap low-resolution sensor is a
challenging task. Existing rigid registration methods failed to use the
physical 3D uncertainty distribution of each point from a real sensor in the
dynamic alignment process mainly because the uncertainty model for a point is
static and invariant and it is hard to describe the change of these physical
uncertainty models in the registration process. Additionally, the existing
Gaussian mixture alignment architecture cannot be efficiently implement these
dynamic changes.
  This paper proposes a simple architecture combining error estimation from
sample covariances and dual dynamic global probability alignment using the
convolution of uncertainty-based Gaussian Mixture Models (GMM) from point
clouds. Firstly, we propose an efficient way to describe the change of each 3D
uncertainty model, which represents the structure of the point cloud much
better. Unlike the invariant GMM (representing a fixed point cloud) in
traditional Gaussian mixture alignment, we use two uncertainty-based GMMs that
change and interact with each other in each iteration. In order to have a wider
basin of convergence than other local algorithms, we design a more robust
energy function by convolving efficiently the two GMMs over the whole 3D space.
  Tens of thousands of trials have been conducted on hundreds of models from
multiple datasets to demonstrate the proposed method's superior performance
compared with the current state-of-the-art methods. The new dataset and code is
available from https://github.com/Canpu999
