One way that springs to mind is that, rather than providing the other party with an image, you provide them with a link to a script on your site that produces the image. So while it's producing the image to show on their site, it also updates a log to record that it's been shown. So the link you provide to the other site would include some way to identify that site.
youradserver.php parse the
advert to decide which image to show, and to record the caller.
That may be a horribly outdated way of doing it now.