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You can design a matrix that will remove all color from an image. Try deriving it from rst principles. Shades of gray contain equal amounts of red, green, and blue: black has 0 of each, 50 percent gray has 128 of each (0x808080, 0x80 = 128), and white has 255 of each (0xFFFFFF, 0xFF = 255). So one property of the matrix is that all the equations to determine red, green, and blue channels must be the same, to ensure the output is equal. In matrix terms, this means the rst three rows should be identical. In a grayscale image, there is no hue. There is only the relative lightness or darkness of the pixel. So if you wanted to convert a color image to grayscale, the color of the output pixel should be related to the brightness of the input pixel. A good way to do this is to average the RGB channels. So every gray value is determined by an equal weighting of the brightness of the three color channels. This leads to the simple equation:



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232).

Or, in matrix form:

(16.30)

However, brains are wired to perceive visual reality in a subjective manner. Anyone who s looked at optical illusions knows how subjective vision is. Sometimes what is mathematically precise is not what looks the best. Remember in 35, Programming Vector Graphics, that the default blending mode for gradients is not linear through RGB there, the blending mode that looks best isn t the most mathematically precise. Likewise, you can make a better-looking grayscale image by choosing nonequal bias for each of the red, green, and blue channels. Choosing biases, or luminance coef cients, of 0.3086, 0.6094, and 0.0820, respectively, yields a more natural-looking image. This matrix encodes the constants:





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Denote the bits of 2 as (zo,21,. . ,231). Let in, i l , . . . , ik be a set . of k distinct elements of the set {0,1,2,. . . ,31}. Let E, be the byte that is all 0, except for a 1 in bit i . Then Ei = 231-i. Let

EXAMPLE 37-10

package { import flash.display.Sprite; import flash.filters.ColorMatrixFilter; public class ch37ex10 function ch37ex10() var img:TestImage addChild(img); var grayMat:Array extends Sprite { { = new TestImage();

(5.57)

= [0.3086, 0.6094, 0.082, 0, 0, 0.3086, 0.6094, 0.082, 0, 0, 0.3086, 0.6094, 0.082, 0, 0, 0, 0, 0, 1, 0]; img.filters = [new ColorMatrixFilter(grayMat)];

LP must be minimized with respect to w and b, which requires the gradient of LP to vanish with respect to w and b. The gradients are given by:

} } } import flash.display.Loader; import flash.net.URLRequest; import flash.system.LoaderContext; class TestImage extends Loader {

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< Show that 2 = X + (p << n ) (mod 2 3 2 ) has zero bits in positions i n , i ~ . . . ,ik. Either prove this in general, or show that it , holds for all 1-byte values, with n and k modified accordingly.

EXAMPLE 37-10

(continued)

b. Suppose that we want to force some bits of 2 to be 1 instead of 0. How can be accomplish this by modifying (5.57)

public function TestImage(scale:Number = 1, x:Number = 0, y:Number = 0) { //photo (CC-BY) Roger Braunstein //source http://www.flickr.com/photos/rogerimp/2940373537/ var url:String = "http://actionscriptbible.com/files/heiwadoori.jpg"; load(new URLRequest(url), new LoaderContext(true)); scaleX = scaleY = scale; this.x = x; this.y = y; } }

s = 1 p (16.31)

Converting an image to grayscale is a special case of modifying the saturation of an image. Saturation measures the amount or vividness of color in an image; converting to grayscale is called desaturation because, of course, it removes all color from an image. But you can modify the saturation of an image with more accuracy than simply all-or-nothing. Changing the saturation does two things simultaneously. It tones down each channel in much the same way that you scaled brightness (although this time you re going to use the luminance coef cients instead of giving each channel equal weight). At the same time, changing the saturation gives each channel an extra dose of its own color. In other words, it turns up the color of each channel while turning down the brightness overall to compensate. To calculate the red channel with a saturation scale factor of s, and the luminance coef cient constants 0.3086, 0.6094, and 0.0820 given by rw, gw, and bw, the equation is

2 ).

Every channel is scaled down as the saturation scales up, but the red channel is scaled up. In other words, the contribution of each color to its own channel is emphasized, enhancing the saturation of each color. Example 37-11 changes the saturation of the image with the x position of the mouse.

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