I run into an issue that might be obvious to some… Never the less here it is.
I created a scene with a background image, labels, which have a PerspectiveTransformation applied to them, and Polygon shapes over the transformed labels, so I can have hover over the polygons and simulate an action of the label. Everything looked fine. However I never hovered over one of the polygons. I then added another polygon in the middle to the root StackPane. There happened the most curious thing: I only could hover over it when I moved in from the left side. This got me thinking, that there is probably some component on top, which has a transparent part there. Adding the polygon as the very last component confirmed this assumption. So add your components to the stack in the correct back to front order to avoid issues like this.