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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

The single-factor analysis of variance model developed in 13 for comparing a population means is e i j 1, 2, . . . , a 1, 2, . . . , ni

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.

/ / If the node that sent this message is also selected / / for visualization, update its log in 'real time' if (Integer.parseInt((String) i d L i s t . g e t S e l e c t e d I t e m 0 ) magorigin)

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EXAMPLE 37-11

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In this model, the error terms ij are assumed to be normally and independently distributed with mean zero and variance 2. The assumption of normality led directly to the F-test described in 13. The Kruskal-Wallis test is a nonparametric alternative to the F-test; it requires only that the ij have the same continuous distribution for all factor levels i 1, 2, . . . , a. a Suppose that N g i 1 ni is the total number of observations. Rank all N observations from smallest to largest, and assign the smallest observation rank 1, the next smallest rank 2, . . . , and the largest observation rank N. If the null hypothesis H0: ...

package { import flash.display.Sprite; import flash.events.MouseEvent; import flash.filters.ColorMatrixFilter; public class ch37ex11 extends Sprite { protected var img:TestImage;

is true, the N observations come from the same distribution, and all possible assignments of the N ranks to the a samples are equally likely, we would expect the ranks 1, 2, . . . , N to be mixed throughout the a samples. If, however, the null hypothesis H0 is false, some samples will consist of observations having predominantly small ranks, while other samples will consist of observations having predominantly large ranks. Let Rij be the rank of observation Yij, and let Ri. and Ri . denote the total and average of the ni ranks in the ith treatment. When the null hypothesis is true, E1Rij 2 and E1Ri.2 1 ni ni ja E1Rij 2 1 N 2 1 N 2 1

The Kruskal-Wallis test statistic measures the degree to which the actual observed average ranks Ri . differ from their expected value (N 1) 2. If this difference is large, the null hypothesis H0 is rejected. The test statistic is

function ch37ex11() { img = new TestImage(); addChild(img); addEventListener(MouseEvent.MOUSE_MOVE, onMouseMove); } protected function onMouseMove(event:MouseEvent):void { //1 for no change, 0 for desaturate, >1 for high saturation //mouse at left for grayscale, right for 3x saturation boost var s:Number = stage.mouseX / stage.stageWidth * 3; var R:Number = (1 - s) * 0.3086; var G:Number = (1 - s) * 0.6094; var B:Number = (1 - s) * 0.0820; var satMatrix:Array = [R+s, G, B, 0, 0, R, G+s, B, 0, 0, R, G, B+s, 0, 0, 0, 0, 0, 1, 0]; img.filters = [new ColorMatrixFilter(satMatrix)]; } } } import flash.display.Loader; import flash.net.URLRequest; import flash.system.LoaderContext; class TestImage extends Loader { 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; } }

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