How to get quality of image in PHP

Chances are they are simply using a standard compression or working on some very simple rules to calculate image compression/quality. It isn't exactly what you were after but what I often use on uploaded images etc etc dynamic content is a class called SimpleImage:

http://www.white-hat-web-design.co.uk/blog/resizing-images-with-php/

this will give you the options to resize & adjust compression, and I think even change image type (by which I mean .jpg to .png or .gif anything you like). I worked in seo and page optimization was a huge part of my Job I generally tried to make the images the size the needed to be no smaller or bigger. compress JS & CSS and that's really all most people need to worry about.

It looks like you could use the PageSpeed Insights API to get the compressions scores: https://developers.google.com/speed/docs/insights/v1/reference, though I'm guessing you'd want to run a quality check/compression locally, rather than sending everything through this API.

It also looks like they've got a standalone image optimizer available at http://code.google.com/p/page-speed/wiki/DownloadPageSpeed?tm=2, though this appears to be a Windows binary. They've got an SDK there as well, though I haven't looked into what it entails, or how easy it would be to integrate into an existing site.