In theory there is no minimum height due to the way that the visual beam is created; it is projected via a focussing lens.
Visual segment is defined by the glare-shield cut-off angle, aircraft attitude, and slant visibility; perhaps this isn’t the term you require.
The important difference, as above, is in the wheel-to-eye height which determines the wheel-height over the threshold. At some major airports, there is a second set of PAPIs installed further into the runway for long body aircraft, following these better optimises the threshold crossing height.