While distinguishing dark from light may sound like an easy task, it's harder than it sounds. The images are in fact many shades of gray, with blurry patches. "It's not all that easy even for a person," said Horowitz. "The rule of thumb is, anything that involves prior knowledge or interpretation, and that's difficult for a person, is at least very difficult for a computer." The reason, Horowitz explained, is that any information given to a computer must be extremely precise in order for the machine to be able to use it. "The machine does not like ambiguity," said Horowitz.
Although the MRI captures a "slice" of the brain and reveals lesions, it's important to remember that both the brain and any lesions are actually three-dimensional objects, Horowitz noted. Mathematics is integral to computer imaging for several reasons, according to Horowitz. First, in order to give a computer instructions, those instructions must be expressed in mathematical terms. Also, MRI formation relies on quantum physics, according to which protons in the body act like tiny magnets. What makes the MRI work is our ability to encode the behavior of the protons mathematically, and then create an image based on that mathematical statement. "Statistics comes into the picture because there's an intrinsic element of randomness at the quantum level and also in the formation of the image," Horowitz added.
Eventually, researchers hope, a physician will view a computer image of the
brain, and circle a region containing a suspected lesion with a computerized
"pen." This would enable the machine to focus on
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Contact: Joseph Horowitz
joeh@math.umass.edu
413-545-6012
University of Massachusetts at Amherst
23-Jun-1999