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When images are captured as digital bits of information, they can be improved by software, opening up a whole new world of possibilities. For the past 15 years or so, says Raskar, researchers have been working to take full advantage of those possibilities, especially through new image processing algorithms that borrow from the traditionally distinct fields of computer vision and computer graphics. Computer vision enables a camera to analyze objects in a picture, picking out features like the edge of a table. And the techniques of computer graphics offer numerous ways to manipulate a digital image. When these approaches are combined in a camera whose optical components are designed with such algorithms in mind, you can do some surprising things. For example, you can, in effect, adjust the light source after the photo has been taken, so that an object lit from one angle appears to be lit from another. And you can even adjust the focus on a photograph after the fact.

Battling motion Blur

One of the most compelling examples of what computational photography can achieve is motion-invariant photography, a clever way of eliminating blur from pictures of moving objects.

“Blur is a process that scrambles information,” says Frédo Durand, an MIT associate professor of electrical engineering and computer science who has helped develop this idea. Pixels of a digital image behave just like squares on a checkerboard, he says. A rapidly moving black-and-white checkerboard pattern blurs to gray, an average of the black and white squares. But if you know precisely how the checkerboard was moved–say, by spinning it around a point in the center, or by shaking it up and down–then you can write a mathematical function to describe the motion-based blur. Once you know that function, you can invert it to remove the blur.

Durand and his colleagues–including Anat Levin, a postdoctoral fellow, and Bill Freeman, an MIT professor of electrical engineering and computer science–have designed a camera that can take advantage of this principle to remove blur from a picture of an object that’s traveling in a straight line, such as a car speeding down the road. The key is to do something counterintuitive, Durand says: “We create more blur by moving the camera during exposure.”

The researchers’ test camera has an optical system that moves back and forth along a straight line, blurring the entire image. Because of the way the sensor is moving back and forth, there will be at least one moment during the exposure when the camera is perfectly tracking the photographed object, allowing the camera to capture accurate information about the object’s visual structure, regardless of its velocity. This information enables the researchers to write an equation defining the motion-based blur–and then to eliminate the velocity from that equation. By inverting the equation, they can reconstruct an image without any blur at all (see “Eliminating Motion Blur,” p. M14).

In this camera, unlike a typical model, “the job of the optics isn’t to directly form the final image,” Durand says. Instead, in a sense, it’s to “shuffle the light rays so what’s recorded by the sensor gives us access to more information.

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