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New Twist on Paint-By-Numbers

Mathematician Dan Rockmore, Dartmouth College, uses digital images to authenticate old paintings. For example, New York’s Metropolitan Museum of Art has asked him to determine which of the 42 "Rembrandt" paintings it owns are authentic.

Rockmore explains the process: "The fact that you can put everything on the computer means that everything is numbers. As soon as everything is numbers, it makes perfect sense to ask mathematical questions about what the numbers represent." A lot of money is riding on this process.

The four steps of authentication: digitize the artwork, convert the image to grayscale and segment it into squares, use software to search for patterns indicating the artist’s style, and finally plot points on a 3D grid and compare them to points produced by other paintings. Graphing points for a particular artist's works will cluster together, if they are authentic.

For example, one of his tasks was to determine the number of different artists that contributed to the painting "Madonna with Child" by Perugino.

To see the actual mathematics used and his conclusions, refer to his joint paper "A Digital Technique for Art Authentication".

Source: B. Trivedi's "The Rembrandt Code," Wired, 12/2005, pp. 276-282