Retrieve computed value from background-size:cover/contain

I know I’m very late to the party but i have used the code below to solve this.

    var backgroundImage = new Image();
    backgroundImage.src = $('my_div_id').css('background-image').replace(/"/g,"").replace(/url\(|\)$/ig, "");

    backgroundImage.onload = function() {
        var width = this.width;
        var height = this.height;

        var object = $('#my_div_id');

        /* Step 1 - Get the ratio of the div + the image */
        var imageRatio = width/height;
        var coverRatio = object.outerWidth()/object.outerHeight();

        /* Step 2 - Work out which ratio is greater */
        if (imageRatio >= coverRatio) {
            /* The Height is our constant */
            var coverHeight = object.outerHeight();
            var scale = (coverHeight / height);
            var coverWidth = width * scale;
        } else {
            /* The Width is our constant */
            var coverWidth = object.outerWidth();
            var scale = (coverWidth / width);
            var coverHeight = height * scale;
        }
        var cover = coverWidth + 'px ' + coverHeight + 'px';
        alert('scale: ' + scale + ', width: ' + coverWidth + ', height: ' + coverHeight + ', cover property: ' + cover);
    };

A detailed walkthrough can be found here http://www.gene.co.uk/get-computed-dimensions-background-image-background-size-cover/