objects do exist independently of our perception of them. i know there's some experiments in physics that seem to question this, but getting to the conclusion that there isn't an independent, objective reality is just a bad interpretation, relying more on assumptions than observation.
however, objects also exist in our minds in subjective ways that differ from that objective interpretation. and, depending on the subject, the objective interpretation may be so poorly defined that only the subjective interpretation is meaningful in any definable context.
abstractly, there's no contradiction in this. the confusion arises from the misunderstanding that things can only exist subjectively or objectively. that merely reduces to human arrogance. the way we interpret things in our minds has no effect on the reality that exists beyond us. but, we're likewise simply not able to grapple with many things beyond what we can subjectively interpret them as, due to the sum of our experience and knowledge. so, there arises what seems like a functional contradiction, but it is really only the result of incomplete knowledge.
this seeming contradiction defines most of the relationships we have, in every context. the person in front of you has an objective existence, but you're only able to comprehend that person through the lens of your subjective experience with that person, thereby making your interpretation of them incomplete at best and just flat out wrong at worst (which, unless you know somebody very well, is usually going to be the case). and, we will absolutely place people into boxes in order to categorize them and make sense of them, in ways that only partially conform to the evidence we have in front of us - because we are not perfect logical machines, but imperfect biological creatures.
even more muddying is that our perceptions of ourselves go through the same filters. you can only understand yourself through the same subjective process. you can not know yourself objectively.
so, what is the objective object, then? it exists, but it's not possible to measure it. maybe a trafalmadorian could figure it out by observing it from a fourth dimension. but none of us ever can.
but we should be aware that it exists, so as to not become too confused by the imperfect lenses we have to experience objects with.
in my view, that's a really final conclusion to this problem.
in that sense, i am absolutely a creation of your imagination - an idea.
but i am also a creation of everybody else's imagination, including my own imagination.
and you are a figment of my imagination, as you are a figment of everybody else's imagination, including your own imagination.
but we all also exist objectively and independently of anybody's imagination. it's just that none of us can ever measure that without breaking the rules and limitations of consciousness.