How to prevent holes that makes the displacement modifier? I made a displacement texture and it looks fine, but when I apply it with the displacement modifier, there are this hole outlines that is surrounding every object.
How to prevent the modifier from making those holes?

This is the texture -
On the Displacement Modifier, you can change the strength to a negative value.



EDIT:
You'll get what you are looking for if you modify the image that you're using to drive the displacement so that the value for the plane in isn't gray, but black. 

Think of it this way: Black becomes the lowest point in the displacement and white the highest.