Differences in the sky coordinates across the Hubble and the Gaia sources. Each point corresponds to the R.A. and decl. coordinate differences in a particularly challenging field. The left panels show the offset vectors across associations (within a search radius) in the original Hubble and Gaia catalogs. The right panels illustrate the same after the robust transformation is performed. The center red points correspond to the associations that our procedure flags as good matches, which are also shown in detail in the bottom panels. Despite an offset of over 90 arcsec between the two catalogs, we have not only found the correct associations but the overall transformation also makes the good matches a tighter scatter, see the comparison in the bottom two panels.