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Math Trek

Computing Photographic Forgeries

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2:04pm, March 15, 2007
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Last August, a photograph from Reuters appeared in newspapers around the world showing smoke plumes billowing from buildings after an air strike in Beirut. Bloggers soon noticed a strange repeating pattern in the smoke. A portion of the photograph, they said, had been copied and repeated in the picture, exaggerating the amount of smoke and destruction.

Reuters rapidly admitted that the photograph had been faked and removed it, along with 920 other images from the same photographer. It was a precautionary move to avoid using photos of uncertain authenticity. The episode left Reuters and other news organizations worried about inadvertently publishing altered photographs.

Hany Farid, a computer scientist at Dartmouth College, is bringing mathematics to the rescue. He has created mathematical tools to determine whether a digital photograph was altered after being taken. His methods work so well that the Associated Press now asks him to scrutinize any photo that seems fishy.

"We've developed a bag of tricks," Farid says. "Every time somebody tampers with a photograph, we try to understand what they did and how to detect it."

In tampering with the Reuters photograph the forger used "copying and pasting," a common forgery technique. A forger may also use copying and pasting to remove a person's image from a photograph by covering it. In either case, Farid's software can identify the forgery by detecting repetitions in the digital bits that comprise the image—even if those repetitions are too subtle for the eye to detect.

Another way to doctor an image is to piece together two separate photographs. For example, during the 2004 presidential campaign, an image surfaced on the Web showing John Kerry speaking with Jane Fonda at an anti-war demonstration in the 1960s, complete with an Associated Press insignia. Some veterans of the Vietnam War reacted with rage at seeing the presidential candidate sharing a stage with the controversial actress and anti-war activist. But the picture, it turned out, was a fake.

"Even after it was determined that it was a fake, people were still talking about Kerry at a war rally," says Farid. "The power of the images stays with us."

In this case, the original photographers recognized that their own work had been altered, thus exposing the forgery. However, Farid could also have detected the forgery by analyzing the pixels. In the originals, Kerry and Fonda were different sizes, so the forger had to rescale Fonda to put her into the photograph with Kerry. That rescaling leaves a telltale signature in the pixels.

Farid also analyzes the light in photographs to see if the light source is the same across different portions of the image. One way of doing that is to study the shadows to extrapolate where the light must have been coming from. Another way is to study the dots in people's pupils.

"The eyes are a partial mirror into the world in which you're photographed," Farid says. If there are two white dots in each eye, there had to have been two separate light sources. So, if a photo shows two dots in one person's eyes and only one dot in another person's eyes, it must have been spliced together from two different originals.

Also, the color of the light determines the dots' precise shade of white. A composite image from different photographs may have shades that vary from person to person.

Each latest version of Photoshop has new tools that allow for better forgeries, so Farid continually needs to figure out new methods.

"This is an arms race," Farid says. "I can already tell you how it's going to end: We're going to lose. It's always going to be easier to create a forgery than detect a forgery. But we're going to take the power to create forgeries out of the hands of amateurs. We will raise that bar up until you have to be very, very good to do it."


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