Four observers, one Ω

Same group photograph — four different equivalence relations — four different quotient geometries. What is each observation map?

Group photo

Ω — 10 people, 1 photograph

A
B
C
D
Each bar is one equivalence class. Each histogram comes from a different observer X acting on the same Ω.

Can you identify the quotient map X → Ω/~ for each?

Observational Geometry — C. Lee-Jenkins  |  The geometry of inference