function bg_img_resize() {
    var w = $(window).width();
    var h = $(window).height();
    var iw = $('#the-background img').attr('width');
    var ih = $('#the-background img').attr('height');
    var rw = iw / ih;
    var rh = ih / iw;
    var sc = h * rw;
    if (sc >= w) {
        nh = h;
        nw = sc;
    } else {
        sc = w * rh;
        nh = sc;
        nw = w;
    }
    $('#the-background img').css({height: nh, width: nw});
}

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