Figure 77 Sample Quantization Tables from the JPEG Standard in .NET framework

Generate QR in .NET framework Figure 77 Sample Quantization Tables from the JPEG Standard
Figure 77 Sample Quantization Tables from the JPEG Standard
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Cb and Cr Component Quantization Table
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oldroad
Zigzag Ordering
-38 -9 -3 4 -2 -1 0 0
Figure 78 Quantized DCT Coefficients from Figure 76
18 -8 -2 4 -1 0 0 0
1 1 0 0 0 0 0 0
-3 3 1 -1 0 0 0 0
-1 1 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
The result from quantizing sample values from Figure 76 with the sample Y quantization table in Figure 77 is shown in Figure 78 After quantization only 19 out of 64 DCT coefficients values are nonzero 8 covers how JPEG compresses runs of zero AC coefficient values
Zigzag Ordering In order to group as many of the quantized zero-value coefficients together to produce the longest runs of zero values, AC coefficients in a data unit are encoded using a zigzag path Figure 79 shows the zigzag order defined by the JPEG standard This was briefly mentioned in 5 in the section on the DQT marker Quantization values within quantization tables are stored in JPEG files using this zigzag ordering also This is the ordering of the quantized AC coefficients in Figure 78: 18 -9 -3 -8 1 -3 1 -2 4 -2 4 0 3 -1 0 1 1 0 -1 -1 0 0 0 -1 (39 Zeros)
Figure 79 Zigzag Order for AC Coefficients
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The Discrete Cosine Transform
Conclusion In this chapter we described the Discrete Cosine Transform (DCT) and quantization The DCT is used to represent an 8 x 8 block of sample values as a sum of cosine functions The DCT coefficient in the upper left corner represents a constant value and is known as the DC coefficient All other coefficients are AC coefficients We used matrix operations to calculate the DCT and its inverse In 10 we will take another look at the DCT and show how it is possible to make it faster More information on the DCT can be found in Rao and Yip (1990), an entire book devoted to the subject Nelson (1992) presents a simplified, JPEG-like version of DCT compression The sample quantization tables in this chapter come from JPEG (1994) Any introductory book on linear algebra, such as Anton (1981), will contain more information on basic matrix operations The source code for this chapter consists of classes for representing quantization tables and data units during compression These classes use matrix operations to implement the DCT
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8
Decoding SequentialMode JPEG Images
We dealt with most of the JPEG preliminaries in previous chapters This chapter puts the pieces together and shows how to implement a sequential-mode JPEG decoder We will cover SOF0 (baseline DCT) frames and a subset of SOF1 (extended sequential DCT) frames These are identical except that extended sequential frames can use 12-bit or 8-bit samples and up to four DC or AC Huffman tables, whereas baseline DCT JPEG supports only 8-bit samples and up to two DC and AC Huffman tables If we limit ourselves to 8-bit samples and permit up to four DC or AC Huffman tables, these two frame types are decoded in exactly the same manner
MCU Dimensions JPEG compressed data consists of a sequence of encoded MCUs arranged from top to bottom, left to right The first step in decoding scan data is to determine the number of data units from each scan that make up each MCU and the number of MCUs required to encode the scan For any component, the number of pixels a data unit spans is Pixelsx = 8 Pixelsy = 8 where