How to filter out selective resources from being served by CDN?

Would like to know if a web-server can control the resources (selectively) which are going to be served by a CDN ? Example, I don't want a specific image to be served by CDN. All other resources except the specific image should be served by CDN.

Can this sort of communication even be established ? Are there any specifications around it ?

Tried searching about integration between a site and CDN. Seems very hard to get plain and simple explanation around the same. Any insights appreciated.