how to find if a photo has been Photoshopped or not with math? here even the minor changes are not visible to the naked eye

Ann Dooms is a mathematician who specializes in forensics of a very specific kind — multimedia. The Vrije University Brussel researcher uses clever math to analyze digital media — photos and videos — and search out foul play. “We play our daily episode of ”CSI: Multimedia,’” she explains in a talk at TEDxBrussels, exploring the ways she and her team at the university work on forensics projects.

How does multimedia forensics work?

This is a photo of a cat.

Zoom in.

No, really.

Here is what those pixels look like when encoded by color:

These numbers offer Dooms a grand opportunity … for math.

Algorithms can be used to find “patterns, irregularities, additions, and changes,” she says, like …

in these two photos:

 which may look the same, but … the numbers say otherwise.

Here are the photos in numbers:

And here are the inconsistencies in those numbers:

reflecting changes that Dooms made to the colors in the photos “that are barely noticeable to the naked eye,” but allow Dooms to do things like hide an entire cat in a scattered image: