Brightness constancy is whenever we perceive an object as having constant lightness while the illumination varies.
As a real example on the left, we see that there are two gray squares inside of a black and a lighter gray square. The two squares appear to be different shades of gray, but are really the same shade. Brightness constancy helps us to see that despite the different reflections the outer square gives on the inner square, the inner squares are still the same shade.
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