title: Finding the relative shift and rotation that gives the maximum overlap for two point-clouds
body: <p>I have two pointclouds in a 3D euclidean space, and I want to find the relative rotation and translation between the two pointclouds that gives the most overlap (or in other words, that minimizes the Wasserstein Distance, or any other optimal-transport metric, between the pointclouds).</p>
  <p>I know that for translation one would simply shift the &quot;center of mass&quot;. However rotation doesn't seem very intuitive to me.</p>
  <p>What I have tried:</p>
  <p>My approach was to compute the inertia tensor and rotate the point clouds to align their principal axes. However this is numerically unstable for pointclouds with high degrees of symmetry.</p>