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It can extend the colors at the edge of the image to outside the image This is called clamping In this case, the value i corresponds to the pixel labeled 41, even though you ve already used that pixel with the f coef cient You simply extend the edges of the image down and to the left (or in other directions, when you re processing a pixel on other edges of the image) as far as necessary to provide a corresponding value for every coef cient in the convolution matrix The alternative is to use a prede ned color value for all pixels outside the de ned image You can choose whether to clamp the image or use a preset value with the clamp Boolean property of a ConvolutionFilter The lter uses clamping by default.

(15-13)

Note that S 2 is just the variance of the ranks. When the number of ties is moderate, there will be little difference between Equations 15-11 and 15-12 and the simpler form (Equation 15-11) may be used. EXAMPLE 15-7 Montgomery (2001) presented data from an experiment in which ve different levels of cotton content in a synthetic ber were tested to determine whether cotton content has any effect on ber tensile strength. The sample data and ranks from this experiment are shown in Table 15-4. We will apply the Kruskal-Wallis test to these data, using 0.01.

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When set to false, you can provide the out-of-bounds color with the color and alpha properties You provide the matrix to this lter as a one-dimensional array with the matrix contents in row-major order, left to right and top to bottom You tell the ConvolutionFilter what dimensions to interpret your matrix as with its matrixX and matrixY properties For example, to de ne the following 3 5 matrix.

Table 15-4 Data and Ranks for the Tensile Testing Experiment Percentage of Cotton 15 ranks 20 ranks 25 ranks 30 ranks 35 ranks y1j r1j y2j r2j y3j r3j y4j r4j y5j r5j 7 2.0 12 9.5 14 11.0 19 20.5 7 2.0 7 2.0 17 14.0 18 16.5 25 25.0 10 5.0 15 12.5 12 9.5 18 16.5 22 23.0 11 7.0 11 7.0 18 16.5 19 20.5 19 20.5 15 12.5 9 4.0 18 16.5 19 20.5 23 24.0 11 7.0 ri. 27.5 66.0 85.0 113.0 33.5

you would use the following code:

Since there is a fairly large number of ties, we use Equation 15-12 as the test statistic. From Equation 15-13 we nd s2 1 N c r2 1 ia ja ij 1 1 251262 2 d 2

var f:ConvolutionFilter = new ConvolutionFilter(); f.matrixX = 5; f.matrixY = 3; f.matrix = [a,b,c,d,e,f,g,h,i,j,k,l,m,n,o];

12 2

It s important to set the dimensions of the input matrix before setting the matrix. You may also set all three at the same time using ConvolutionFilter s constructor. Here are the properties of ConvolutionFilter:

12 2

Figure 4.18 Processing the messages received from sensor nodes. The messageReceived0 function of the Mainwindow class.

1 c 5245.7 53.54 19.06

matrixX Number of columns in the convolution matrix. matrixY Number of rows in the convolution matrix. matrix Array de ning the elements of the convolution matrix. Its size must correlate to the dimensions provided by matrixX and matrixY. divisor Number that the sum of the pixel contributions is divided by. bias Number added to the sum of the pixel contributions. preserveAlpha Whether to apply the convolution to alpha values. When true, the result of the convolution affects only the red, green, and blue channels, and alpha values are unchanged. Defaults to true. clamp Whether to clamp edges of the image. Defaults to true. color If clamp is false, the out-of-bounds color as a uint. alpha If clamp is false, the alpha of the out-of-bounds color.

2512622 d 4

Like other lters, these parameters may be provided to the constructor in this order, and all are optional. Convolution matrices are used in computer vision and computer graphics because they are fast and versatile. You can use different matrices to sharpen an image, blur it, detect and enhance edges, do cheesy embosses and bevels, or create other effects that operate on local features of the image.

2 Since h 13.28, we would reject the null hypothesis and conclude that treatments 0.01,4 differ. This same conclusion is given by the usual analysis of variance F-test.

Under certain conditions, 3 3 convolution matrices are accelerated if your processor supports a certain extended instruction set. Check the AS3LR under the matrix property of ConvolutionFilter for details.

15-5.2

EXAMPLE 37-12

The procedure used in the previous section whereby the observations are replaced by their ranks is called the rank transformation. It is a very powerful and widely useful technique. If we were to apply the ordinary F-test to the ranks rather than to the original data, we would obtain F0 1N H 1a 12 1 H2 1N

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