Why does gamma correction of image use two different definitions of gamma?

I've noticed that the gamma value used in level adjustment of Photoshop and Canvas is 'opposite' of gamma values defined in Wikipedia or MATLAB imadjust documentation.

In Wikipedia or MATLAB, high gamma (>1) will make an image darker, whereas in Photoshop high gamma (>1) will make an image brighter.

I've also noticed that, even among image processing software, Zeiss' Zen software uses high gamma (>1) to make an image darker.

There seem to be two definitions of gamma value. This is just confusing... I assume that this is related to 'gamma encoding' and 'gamma correction'. But can anyone explain the rationale of these two defintions and when to use which one?

Vout = Vin ^gamma % Wikipedia or MATLAB


Vout = Vin ^1/gamma % Photoshop or Canvas