In short, no generic ways. It has so called "generic" way for Youtube or Vimeo simply because these sites have standard URL formats for high res video, and the script is clever enough to build the URL from existing information in the web site (e.g. some patterns)
For images...
If it's targeting generic web sites using some popular image hosting services like Flickr, it may be possible to get the high res image URL from thumbnail one.
If it's targeting a specific website using less popular image hosting service, or it hosts images in their own web servers, it may be possible to check for common patterns in the site to find out the URL of high res image.
If it's targeting generic web sites using less popular image hosting service or self-image-hosting, basically the script needs to be intelligent enough to guess or find out the high res URL from information in the page. It may not always work because some sites built the URL dynamically using Javascripts or even display images in browser plugins like Flash...