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Appendix E
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way, pixels in a video image typically have similar pixels all around them. To make use of these neighborhood relationships, it is desirable to transform not only in lines and columns, but also in areas. This can be achieved by a planar transform. In practice, separable transforms are used almost exclusively. A separable planar transform is nothing more than the repeated application of a simple transform. It is almost always applied to square picture segments of size N N, and it progresses in two steps, as illustrated in Figure E.2. First, all lines of the picture segments are transformed in succession, then all the rows of the segments calculated in the first step are transformed.
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Figure E.2 A simplified search of a best-matched block. (From [2]. Used with permission.)
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In textbooks, the planar transform is frequently called a 2D transform. The transform is, in principle, possible for any segment forms, not just square ones [4]. Consequently, for a segment of size N N, 2N transforms are used. The coefficients now are no longer arranged as vectors (i.e., a list of values), but as a matrix (i.e., a table). The coefficients of the i lines and j columns are called cij (i,j 1 N). Each of these coefficients no longer represents a basic vector, but a basic picture. In this way, each N N picture segment is composed of N N different basic pictures, in which each coefficient gives the weighting of a particular basic picture. Figure E.3 shows the basic pictures of the coefficients c11 and c23 for a planar 4 4 DCT. Because c11 represents the dc part, it is called the dc coefficient; the others are appropriately called the ac coefficients. The planar transform of television pictures in the interlaced format is somewhat problematic. In moving regions of the picture, depending on the speed of motion, the similarities of vertically neighboring pixels of a frame are lost because changes have occurred between samplings of the two halves of the picture. Consequently, interlaced scanning may cause
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Figure E.3 The mechanics of motion-compensated prediction. Shown are the pictures for a planar 4 4 DCT. Element C11 is located at row 1, column 1; element C23 is located at row 2, column 3. Note that picture C11 values are constant, referred to as dc coefficients. The changing values shown in picture C23 are known as ac coefficients. (From [2]. Used with permission.)
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the performance of the compression system (or output concentration) to be greatly weakened, compared with progressive scanning. It is for this reason that most commercial streaming media encoders include a deinterlacing option, prior to compression. MPEG-2 and MPEG-4 also require deinterlaced images. Well-tuned compression algorithms try to detect stronger movements and switch to a transform in picture one-half (i.e., field) for those picture regions [5]. However, the coding in one-half of the picture is less efficient because the correlation of vertically neighboring pixels is weaker than in the full picture of a static scene. Simply stated, if the picture sequences are interlaced, the picture quality may be influenced by the motion content of the scene to be coded.
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With common algorithms, compression ratios of approximately 8:1 can be achieved while maintaining good picture quality [2]. To achieve higher compression ratios, the similarities between successive frames must be exploited. Not only does every pixel in a frame of video have similar pixels all around it, it also has similar pixels in the same relative screen
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Appendix E
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positions as itself, in previous and subsequent video frames. The nearest approach to this goal is the extension of the DCT in the time dimension. A drawback of such cubic transforms is the increase in calculation effort, but the greatest disadvantage is the higher memory requirements: for an 8 8 8 DCT, at least seven frame memories would be needed. Much simpler is the hybrid DCT, which also efficiently codes pictures with moving objects. This method comprises, almost exclusively, a motion-compensated difference pulse-code-modulation (DPCM) technique; instead of each picture being transferred individually, the motion-compensated difference of two successive frames is coded. DPCM is, in essence, the predictive coding of sample differences. DPCM can be applied for both interframe coding, which exploits the temporal redundancy of the input image, and intraframe coding, which exploits the spatial redundancy of the image. In the intraframe mode, the difference is calculated using the values of two neighboring pixels of the same frame. In the interframe mode, the difference is calculated using the value of the same pixel on two consecutive frames. In either mode of operation, the value of the target pixel is predicted using the reconstructed values of the previously coded neighboring pixels. This value is then subtracted from the original value to form the differential image value. The differential image is then quantized and encoded. Figure E.4 illustrates an end-to-end DPCM system.
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