var bgImage = $('#background-image');	

$(document).ready(function() {
    resizeImg();
    $(window).resize(function() {
      resizeImg();
    }); 
});


function resizeImg() {
  var imgwidth = bgImage.width(),
	   imgheight = bgImage.height(),
	   winwidth = $(window).width(),
	   winheight = $(window).height(),
	   widthratio = winwidth / imgwidth,
	   heightratio = winheight / imgheight,
	   widthdiff = heightratio * imgwidth,
	   heightdiff = widthratio * imgheight;

  if(heightdiff>winheight) {
	bgImage.css({
	  width: winwidth+'px',
	  height: heightdiff+'px'
	});
  } else {
	bgImage.css({
	  width: widthdiff+'px',
	  height: winheight+'px'
	});
  }

 $("#background-image").show();

}