The only fair answer is “it depends.”
If I were to publish a poem of 16 lines that begins:
…and that is the sole change from a fairly well-known piece entitled “Stopping by Woods…”, I can expect a plagiarism lawsuit from the estate of Robert Frost rather rapidly.
On the other hand, using an image created by someone else with changes to say something entirely different has that aspect of “new creation” necessary for separate copyright.
This is complicated by laws regarding pastiches and parodies. We’ve all, I think, seen that picture of Lisa della Giaconda holding a marijuana joint that amply explains her facial expression, the humor of which lies totally in its being a near-exact copy of the Mona Lisa except for the hand holding the joint. If the Mona Lisa were still under copyright, that would not be a violation, because the point to it is in the identity-with-change parody nature of the “Stona Lisa.”
And one cannot copyright ideas – just what is done with them. The rather famous coincidence of Charles Sheffield and Arthur C. Clarke bringing out simultaneous novels founded in the Beanstalk concept, but doing quite different things with the story, amply explains this.