Resize a div element to its background image size

Question

Is it possible to make a

adapt to its background image? I mean to maintain the proportions width and height.

Clarification:

Answer 1

Maybe using javascript, you can get the url to the image:

var img = document.getElementById('image').style.backgroundImage; 
var width = img.clientWidth;
var height = img.clientHeight;
document.getElemetById('image').style.width = width;
document.getElemetById('image').style.height = height;

I strongly suspect you cannot do this exclusively with stylesheets.