I always do this with Timthumb:
// this is the absolute path
$url="http://crizaze.com/wp-content/themes/joorang/wp-content/uploads/2011/01/ami166a-e1295733091216.jpg";
// convert it into relative path
$url = str_replace(get_bloginfo('url'), '', $url);
// get the image url, resized by timthumb
$timthumb_url = get_stylesheet_directory_uri() . "/timthumb.php?src=$url&w=80&h=80";