Consider these two pixel-oval portals:

  xx         oo
x    x     o    o
x    x     o    o
x    x     o    o
x    x     o    o
  xx         oo

They are the same size, and you can easily make a bijective mapping for each of their pixels.

Rotate one two times in 3D space by 90°, and it fits through the other. If you want more wiggle room, make them taller.