The math behind the feather

A few eagle-eyed readers have written to ask me why feathering blurs a selection outline more than the number of pixels stated in the Feather Radius value. A radius of 4 pixels actually affects a total of 20 pixels: 10 inward and 10 outward. The reason revolves around Photoshop's use of a mathematical routine called the Gaussian bell curve, which exaggerates the distance over which the selection outline is blurred.

Figure 8-13 demonstrates the math visually. The top-left image shows a hard-edged elliptical selection filled with white against a black background. To its right is a side view of the ellipse, in which black pixels are short and white pixels are tall. (Okay, so it's really a graph, but I didn't want to scare you.) Because no gray pixels are in the ellipse, the side view has sharp vertical walls.

The bottom-left image shows what happens if I first feather the selection with a radius of 4 pixels and then fill it with white. The side view now graphs a range of gray values, which taper gradually from black to white. See those gray areas on the sides (each labeled Diameter)? Those are the pixels that fall into the 8-pixel diameter, measured 4 pixels in and out from the original selection outline. These gray areas slope in straight lines.

Figure 8-13: Here are some graphic demonstrations of what happens when you feather a selection. Photoshop tapers the ends of the feathered selections (shown by the black areas, bottom right) to prevent your eye from easily detecting where the feathering starts and stops.

The rounded areas of the side view — painted black — are the Gaussian bell curves. These are appended to the radius of the feather to ensure smooth transitions between the blurry edges and the selected and deselected pixels. Programs that do not include these extra Gaussian curves end up producing ugly feathered selections that appear to have sharp, incongruous edges.

Tip If exact space is an issue, you can count on the Feather command affecting about 2.7

times as many pixels as you enter into the Feather Radius option box, both in and out from the selection. That's a total of 5.4 times as many pixels as the radius in all.

If this was more than you wanted to know, cast it from your mind. Feathering makes the edges of a selection fuzzy — 'nuff said.

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