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Color Quantization The JPEG and PNG formats covered in this book can contain image data that uses 24 bits or more per pixel How can you display a 24-bit JPEG image on an output device that supports only 8 bits per pixel Likewise, how can you convert a JPEG file to the GIF format, which supports a maximum of 8 bits per pixel The answer is a process known as color quantization, a fancy name for the process of reducing the number of colors used in an image The topic of color quantization falls outside the scope of this book; therefore, we are only going to cover enough to allow you to display images if you are using a display that does not support 24-bit images and to convert to such formats The method we are going to use is called median cut quantization In it we create a three-dimensional count of the number of times each pixel color value is used Such a counting would look something like that shown in Algorithm 11 Now we have a cubic region containing all the color frequencies The next step, shown in Algorithm 12, is to divide the cube into two rectangular regions in such a manner that each part has half the frequency values This fragment divides the frequencies in half along the blue axis Figure 111 shows the result of the first application of the process in Algorithm 12 We apply the process recursively, dividing the rectangular regions in half using a different color axis until we have 256 boxes with roughly the same total frequency Figures 112 and 113 show sample divisions of the RGB colorspace along the other axes Keep in mind that this is a rough outline If 4-byte integers were used to store frequency values, the FREQUENCIES array defined in Algorithm 11 would
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Algorithm 77 Gathering Frequencies in the Median Cut Algorithm
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Global FREQUENCIES [0255][0255][0255] Global IMAGE [1IMAGEHEIGHT][1IMAGEWIDTH] Procedure GatherFrequencies Begin For II = 1 To IMAGEHEIGHT Do Begin For JJ = 1 To IMAGEWIDTH Do Begin RED = IMAGE [II][JJ]RED GREEN = IMAGE [II][JJ]GREEN BLUE = IMAGE [II][JJ]BLUE FREQUENCIES [RED][GREEN][BLUE] = FREQUENCIES [RED][GREEN][BLUE] + 1 End End End
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Color Quantization GLOBAL FREQUENCIES [0255][0255][0255] Function DivideBlueInHalf Begin COUNT = 0 For BLUECUT = 0 To 255 Do Begin For II = 0 To 255 Do Begin For JJ = 0 To 255 Do Begin COUNT = COUNT + FREQUENCIES [II][JJ][BLUECUT] End End If COUNT > IMAGEHEICHT * IMACEWIDTH / 2 Then Return BLUECUT End Return 255 End
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Algorithm 12 Dividing the Colorspace in Half
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be 64 megabytes Even in this era of cheap memory, this is too large for a practical implementation In fact, the size of the FREQUENCIES array is larger than the pixel data for most images, so in practice we have to reduce the precision of each color value, use dynamic data structures, or use a combination of both A simple method to reduce the array size is to drop some of the least significant bits from each component value Using 6 instead of 8 bits reduces the size of the FREQUENCIES array to just 1 megabyte (4 26 26 26)
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Figure 111 Example of the RGB Colorspace Being Divided Using the Process in Algorithm 12
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Figure 112 RGB Colorspace in Figure 111, Now Divided along the Green Axis As Well
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Figure 113 RGB Colorspace in Figure 112, Now Divided along the Red Axis As Well
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A Common Image Format A typical application for viewing image files will be able to read and store images using several file formats, and convert files from one format to another Rather than having a function for viewing each type of file and a separate function for each possible format conversion, it is useful to have a common uncompressed image format that can be used for all types of files supported by the application With a common uncompressed format you need only write one display function for the common format If each image file format has a function for reading into the common format and a function for writing from the common format, you have everything you need to display, save, and convert among all file formats
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