There are many ways how you can approach such task and none of them requires detaching polygons. I'm lazy to write detailed description, so i threw quick scene as an example for one of the approach. It's probably not the best method and certainly not the one i would choose myself, but it's one of the easiest to show in one picture without needing to write lengthy description :] You can replace the gradient with custom painted texture, or even with vertex colours if your geometry is dense enough. The most important part here is that you want to have a nice border with 0 displacement in your texture, so there would be no sharp transition between displaced and not displaced parts.