Answer by David for Positioning the pivot point in center in part of mesh

The reason "Origin to Center of Mass" (or "Origin to Geometry") does not work is because your center of mass in not in the same location. The two tiles with dirt, have most of the geometry much lower.

To set the origin in the seam place as the your all green first tile requires a 2 step process.

1. In edit mode, select the top 8 vertices of your tile. (Note that the pivot point can not be set to "3D Cursor" or "Active Element") Now press ShiftS>Cursor to Selected. That will move the 3D cursor to the location you want as the origin.
   

2. In object mode press CtlrAltShiftC>Origin to 3D Cursor.