I have moved this work over to here.
Here I have implemented "Simple Estimation Methods for the Helmholtz – Kohlrausch Effect" by Nayatani.
Running the code generates the following images:
All of the patches in this image have the same Y (luminance) value as the background, however they look very different in terms of brightness thanks to the Helmholtz-Kohlrausch effect.
This shows that luminance is not equal to brightness.
Here I have tried to compensate for the HKE effect using the VCC for luminous colours model from Nayatani. I would say it has overcompensated, as the red, purple and blue look slightly too dark to me.