Physical interaction with the image reveals it to be an illusion, because things can pass through it. A creature that uses its action to examine the image can determine that it is an illusion with a successful Intelligence (Investigation) check against your spell save DC. If a creature discerns the illusion for what it is, the creature can see through the image, and its other sensory qualities become faint to the creature.
The RAW answer seems to be no, even when considering outlandish illusory effects.
A creature can, perhaps, be certain of himself that what he is perceiving is an illusion. However, it seems that the illusion would not appear faint until interacted with or investigated. It does not seem to me that simply by observing an illusion and deducing it for what it is, no matter how sure of himself a creature may be, would constitute interacting with it or (especially important when in combat) investigating it with an action.
Vylix raises a good point in his comment: Being subjected living in a world full of magic, can a creature really know that "something is clearly impossible"? For instance, apple falls to the ground is a nature's law, but having an apple falls to the sky is not at all really impossible, provided there is magic involved: reverse gravity spell.
I've generated some confusion. To clarify:
I'm not asking about whether or not a creature can reach the conclusion that he is looking at an illusion and can react to it logically. A creature certainly can make that conclusion and reaction on his own.
More specifically, I'm asking whether or not the illusion can become faint to that creature simply because that creature is sure of himself that what he is seeing is an illusion. Or, must that creature observe a physical interaction with it, or spend his action investigating to achieve this?
This matters because being able to see through things is important, so is being able to hear things that are masked by illusory sounds, etc. Just because you are not fooled by an illusion, doesn't mean it isn't still interfering with your senses.
Possibly related: this answer to "Are Illusionists subject to their own illusions?".
This answerer suggests that a caster need not interact with or examine his own illusion in order to see through it. There are some ridiculous conclusions to draw here about an illusionist being susceptible in some fashion to his own spells. Perhaps casting an illusion is enough of an interaction so as to reveal it to the caster as fake.
Note that the accepted answer implies a caster may actually be susceptible to his own illusions. I digress.
...Though this question and its accepted answer do not fully address what I'm asking, only how much intent is necessary between an interaction and an illusion.