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tation of the data, with the receiver only recreating an approximation of the original digital media. When we view or hear the good-enough reproduction, our perceptions ignore the deficiencies. In fact, sometimes you can notice that the received digital media is quite unlike the original, because the artifacts are far too obvious to miss. However, being able to transmit an impression of the original may be sufficient, for a given application. Extremely lossy compression can be acceptable in some situations (usually when it s a choice between badly degraded digital media or nothing at all). When a compression algorithm throws data away, it can do it in several ways. Let s consider video compression. First, a compression algorithm can reduce data by quantizing the image more crudely, either by:
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Many algorithms have been derived to perform these operations, ranging from crude select-the-nearest-value approaches, to more sophisticated processing algorithms. The best decimators use sample lattice transforms* to deduce a lesser number of lines, pixels per line, and frames per second from the given sample data (i.e., the data obtained from the analog-to-digital conversion process). Sample lattice conversion produces fewer quantization artifacts than merely choosing some of the available values in the sample set on a nearest-neighbor basis. For a simple reduction in bits per sample value, the crudest way is simply to truncate, whereas the least noticeable way is to dither each value before truncating. Dithering is the process of adding noise to the values in frequency regions that the senses are less attuned to, in order to make the pixel truncation process appear to distort the samples less.
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*If a video sequence is digitally sampled, you get a three dimensional lattice of samples, of dimension pixels per line, by lines per frame, by frames in the sequence. In other words, all the pixel values can be represented as a cubic lattice, with axes representing the dimensions of the video sequence in both space and time. If you need to change the number of frames per unit time, or the number of lines per frame, for example, a sample lattice transform, which is a mathematical algorithm for creating the new sample lattice by three dimensionally interpolating the source lattice sample values, is used. The algorithm has the property of mathematically producing the new sample values in close agreement with what they would have been if the original source video sequence had been sampled according to the dimensions of the final lattice.
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Using fewer bits to represent each color Reducing the number of pixels in the image Reducing the amount the value of a pixel can change compared to its nearest neighbors Reducing the number of frames per second
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Compression algorithms can choose a smaller number of bits to represent a digital symbol denoting pixel values that occur frequently in an image and longer representations for those values that occur infrequently, so that on average you use fewer bits to represent a given moving image. This is called entropy encoding. Entropy encoding is lossless. Huffman codes are an example of entropy encoding. We can exploit features of photographic images, for example, that make it likely that the intensity of a pixel is similar in intensity to its neighbors. Photographic images are said to be Markov sources.* If you know that the next pixel will be similar in intensity to the last, you can use predictive coding schemes, so that given the first pixel, you don t need information about the second, you can just predict its value from the value of the first. In fact, the more you know about the likelihood of the next pixel based on first, second, and higher orders of predictors, the less in error the predicted value will be. In other words, if you can accurately predict the next pixel, given the behavior of several near neighbors, the compression will be better. You can break the picture up into regions and do a transform on each region to establish its frequency domain content. You perform mathematics on the block of pixels in the region to obtain a transform, which gives a spectrum of frequency values that can be represented with fewer symbols than the original block of pixels. Spectral components equate roughly to colors, and transforms establish what colors are present in the block, ignoring the unimportant colors. Further, the base functions of the transform take a given spectral component (a number representing the dominant color in the region analyzed) and fit a pattern to best describe all the pixels in the analysis region with the least error. The compression algorithm has several mosaic tiles representing the transform base functions, which can be thought of as textures. The encoding algorithm takes the actual pixels in a region under analysis and tries to fit the best texture to that block. When a best fit is found, the only data needed for reconstruction of the image are a color value representing the average color in the block and the base function, or texture, which was
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*A Markov source is a source of data that has the property of allowing you to predict the next data value, given the current one, simply because some sequences of values are statistically more likely than others. In the English language, for example, h is more likely to follow t in a word, than say a q. This is because the th letter combination occurs frequently in the English language, whereas the combination tq is very rare. In photographic images, the next pixel is more likely to be close in color to the current one than it is to be a completely different color. Images are just like that. They behave as Markov sources.
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