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CSE679: JPEG

CSE679: JPEG. JPEG goals JPEG compression steps Lab. JPEG Goals. JPEG: Joint Photographic Experts Group Applications can tune compression level Should have tractable computational complexity Should be possible to implement in hardware

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CSE679: JPEG

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  1. CSE679: JPEG • JPEG goals • JPEG compression steps • Lab

  2. JPEG Goals • JPEG: Joint Photographic Experts Group • Applications can tune compression level • Should have tractable computational complexity • Should be possible to implement in hardware • Compression scheme should be independent of data format • PAL/NTSC etc. shouldn’t matter • Independent of picture size, colors etc. • Lossless, hierarchical, sequential, and progressive coding should be possible.

  3. JPEG Compression Steps • Picture preparation • Pixel • Block, MCU (Minimum Coded Unit) • Picture processing • FDCT • Quantization • Entropy encoding • Differential encoding (belongs to Source encoding) • Run-length encoding • Huffman encoding

  4. Picture Preparation • JPEG specifies a very general image model. • A source image consists of at least one and at most 255 components. • Components may be assigned to the three colors RGB, YIQ or YUV signals. • Convert each component into 8 × 8 data blocks • Each pixel is represented by p (8, or 12) bits. • If p = 8, each pixel is an integer in the range of 0 to 255.

  5. Processing – Forward DCT • Shift: The pixel values are shifted into the range [-128, 127]. • DCT expression 7 j

  6. Some Observations of Forward DCT • All 64 values in the input matrix, P[x, y] contribute to each entry in the transform matrix, F[x, y] to generate 64 new samples • F[0,0] is the mean of all 64 values in the matrix, known as the DC coefficient, others are called as the AC coefficients.

  7. DCT Computation Features DCT Computation Features

  8. Quantization • FQ[x, y] = Integer Round (F(x, y)/Q(x, y)) • Different coefficients are treated separately based on quantization table.

  9. An Example of Quantization

  10. An Example of Quantization Table

  11. Entropy Encoding • Vectoring • 2-D matrix should represent the values in the form of a single-dimension vector. • Scan in zig-zag order

  12. Differential Encoding • The DC coefficient varies only slowly from one block to the next. • 12, 13, 11, 11, 10, …… • Only the difference in the preceding block is encoded. • 12, 1, -2, 0, –1

  13. Run-length Encoding • The AC coefficients are encoded in the form of a string of pairs of values (skip, value) • (0,6) (0,7) (0,3) (0,3) (0,3) (0,2) (0,2) (0,2) (0,2) (0,0)

  14. Huffman Encoding • Use variable length codes • Most frequently used symbols coded with fewest bits • The intermediate symbol sequence • DC coefficient: (sss, value) • sss: the number of bits needed • value: the encode value • AC coefficient: (skip, sss) (value) with run-length encoding • skip: the number of consecutive 0s • sss: the number of bits needed to encode the value • value: the encode value • Huffman code • DC coefficients: 12 = (4, 12) = (1011100) • AC coefficient: (0, 6) = (0, 3) (6) = (100110)

  15. Summary • DC coefficient • Input: 12, 13, 11, 11, 10, …… • Differential encode: 12, 1, -1,-1,-2… • The intermediate symbol sequence: (sss, value) • Huffman code: • P160 (b) ⇒ sss • P160 (a) ⇒ value • Example: 12 = (4, 12) = (1011100) • AC coefficient • Input: 6, 7, 3, 0, 0, 3, 3, 2, 0, 0, 0 • Run-length encoding: (0,6) (0,7) (0,3) (2,3) (0,3) (0,2) (0,0) • The intermediate symbol sequence: (skip, sss) (value) • Huffman code: • P163-164 ⇒ (skip, sss) • P160(a) ⇒ value • Example: (0, 6) = (0, 3) (6) = (100110)

  16. Lab Project • Objective: be familiar with JPEG • Description • Input: an original 8 × 8 block ⇒ original data (the value of each pixel is in the range of [0, 255]) (given by the Instructor) • Steps: • Shifted to the range of [-128, 127] • FDCT (round: 1.6 → 2, -1.6 → -2, 1.5 → 2, 1.1 → 1) (π = 3.141592654) • Quantized with the given quantization table (see the given example) (round) (round: 1.6 → 2, -1.6 → -2, 1.5 → 2, 1.1 → 1) • Zig-zag coded • Converted to the intermediate symbol sequence with run-length encoding on AC coefficients • Encoded to bit sequence with Huffman encoding (based on the given default Huffman codewords tables) ⇒ compressed data • The compression ratio = original data size (i.e., 64 × 8)/compressed data size • Output: print out all the results of the above steps into different files (The names and formats of output files should follow the files put on the web.)

  17. Lab Project • Team: 2 or 3 students • What should be turned in (via email to TA, subject: 679 project)? • Put all codes into one file (source_jpeg.c (.cpp) with clear comments (softcopy) • Make sure TA can understand, compile, and run your codes on UNIX machines. All the codes should be in C or C++. • A report including a summary (2 ≤ page # ≤ 5) and the source code file, and result files (hardcopy or softcopy either in PDF) • How will TA grade? • Correctness: TA will use his own data to test your codes. • Clearness: TA will check whether your code and report are understandable. • Fairness: • Students in the same teams get the same scores. • No copy! All students involved in copy will get ZERO.

  18. Example - Original Block

  19. Example - Shifted Block

  20. Example -After FDCT

  21. Example - Quantization Table

  22. Example - After Quantization

  23. Example – Other Steps Zig-zag sequence 62,-4,4,-2,-5,2,-1,3,-3,-1,0,0,0,-1,2,-1,-1,0,1,1,0,1,0,1,-1,-1,1,-1,-1,1,0,0,0,-1,0,0,0,0,0,-1,0,-1,0,0,0,1,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0 Intermediate symbol sequence (6)(62), (0,3)(-4), (0,3)(4), (0,2)(-2), (0,3)(-5), (0,2)(2), (0,1)(-1), (0,2)(3), (0,2)(-3), (0,1)(-1), (3,1)(-1), (0,2)(2),(0,1)(-1), (0,1)(-1), (1,1)(1), (0,1)(1), (1,1)(1), (1,1)(1), (0,1)(-1), (0,1)(-1), (0,1)(1), (0,1)(-1), (0,1)(-1), (0,1)(1),(3,1)(-1), (5,1)(-1), (1,1)(-1), (3,1)(1), (6,1)(1), (1,1)(1), (0,0) Encoded bit sequence (total 154 bits) (1110)(111110) (100)(001) (100)(100) (01)(01) (100)(010) (01)(10) (00)(0) (01)(11) (01)(00) (00)(0) (111010)(0) (01)(10) (00)(0)(00)(0) (1100)(1) (00)(1) (1100)(1) (1100)(1) (00)(0) (00)(0) (00)(1) (00)(0) (00)(0) (00)(1) (111010)(0) (1111010)(0) (1100)(0) (111010)(1) (1111011)(1) (1100)(1) (1010)

  24. Conclusion • JPEG goals • JPEG compression steps • Picture Preparation • Component, block, and pixel • Picture Processing • Forward DCT • Quantization • Different coefficients are treated separately. • Entropy coding • Lab

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