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Part VIII: Graphics Programming and Animation
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Now you ll look at applying a simple convolution matrix to a small image. The convolution matrix is the 3 3 matrix on the left, and the image is the 5 5 image on the right.
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| a b c | | d e f | | g h i | | | | | | 00 10 20 30 40 01 11 21 31 41 02 12 22 32 42 03 13 23 33 43 04 14 24 34 44 | | | | |
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Given this setup, to determine the output of the pixel at (1,1), labeled 11, you would see the following contributions:
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output(1, 1) = a*00 + b*01 + c*02 + d*10 + e*11 + f*12 + g*20 + h*21 + i*22
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In fact, ConvolutionFilter uses this formula but with two changes. You can use a different divisor than 1 for the weighted average. By default, the divisor is 1, so all the coef cients in the convolution matrix should sum to 1 to keep colors in acceptable bounds. But by setting the divisor property, you can choose another number to divide the product above by. The other factor omitted in this formula is a nal offset value to add. This is determined by the value of the bias property of the ConvolutionFilter, which defaults to 0. What happens when you need to calculate the value of the pixel at (4, 0), labeled 40 If you line up the center of the convolution matrix to that pixel, the values a, d, g, h, and i fall outside the image. ConvolutionFilter gives you two options. 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. 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
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| a b c d e | | f g h i j | | k l m n o |
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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];
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37: Applying Filters
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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:
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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.
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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.
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