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Contents:

1. Digital Magic
2. Painting By Numbers
3. A Revealing Image
4. As Easy as Calling Up a Log
5. A Lunar Odyssey
6. Fun with Fuzzy Filters
7. Building Color
8. A Digital Toolbox

Painting By Numbers

Image processing works because, to your computer, a digitized image is nothing but a pile of numbers. When it reads these numbers from a floppy disk or hard drive, your computer doesn't see a picture. All it does is add, subtract, multiply, and divide the numbers that make up the image. Changing the numbers can make the image brighter, give it contrast, or enhance faint structures that are barely visible to the eye.

The simplest change you can make is a linear "stretch." Here's the idea: with an image from a 16-bit CCD camera, for example, the brightness of objects can extend over a range of 65,536 steps. Zero would be pure black, 65,535 would be pure white. If you were to survey all the pixels that make up a typical image of a deep-sky object, you would find that most pixels lie between a low value representing the sky and a high value representing the brightest stars. The brightness of most pixels falls in a narrow range, perhaps no more than 1,000 steps wide, just above the brightness of the sky.

When you first call up your galaxy shot, for example, the computer displays step 65,535 as white. But only a few overexposed stars actually have that brightness. The core of the galaxy has a brightness level of only 1,200. It looks dark gray. The spiral arms are fainter still and barely show up. The sky itself has a level of 200.

What you'd like is to display the sky as black (a screen brightness of 0 percent) and the galaxy core as white (a screen brightness of 100%). To do this you perform a linear stretch. You set 200 to display as 0% and 1, 200 to show as 100 percent, effectively throwing away information in the pixels with values higher and lower than these numbers.

In a linear stretch, the computer assigns a screen brightness of 0 percent to the low pixel value and a screen brightness of 100% to the high pixel value and then creates a table listing all the intermediate pixel values. If the low value is 200 and the high value is 1,200 there are 1,000 pixel values in the image. To stretch the brightness equally between 0 percent and 100 percent, the computer assigns 10 pixel values to each 1 percent increment in display brightness. If you graphed the relationship between the original pixel value and its brightness on your screen, the graph would be a straight line. That's why this stretch is called linear.

Linear stretches work wonders whenever the range of pixel values is fairly short - no more than a few hundred pixel values. This is the case with many faint deep-sky objects and with CCD images that are technically underexposed. A linear stretch takes objects that look dull gray and rescales them over the entire brightness range. Parts that should be bright turn white, while faint parts look dark.

However, when the range of brightness in the original image is wide, too many pixel values must be stuffed into each step in the display brightness scale. Details in the darkest or brightest parts of the image can remain hidden. To extract this detail, you use non-linear stretches.