1. JPEG
Pasi Fränti

2. History of JPEG Standard since 1992 (ISO, CCITT, IEC)
Nothing existed for true color (24-bpp) RGB images. Only method was GIF (8-bits color palette)
Lossy (default) + Lossless (not well known)
Supports also progressive mode
Better methods exists (JPEG 2000, J2K) but JPEG remains the most popular method.
William B. Pennabaker, Joan L. Mitchel
JPEG: Still Imatge Data Compression Standard
Springer Science & Business Media, 1992.

3. JPEG
Compression
Decompression

4. Discrete cosine transform 1-dimensional
DCT transform
Inverse transform
Scaling factors

5. Discrete cosine transform 2-dimensional
DCT transform
Inverse transform 5

6. DCT

7. DCT basis functions N=8 7

8. DCT basis functions 2-dimensional (N=4)8

9. Example blocks Flat
Original
Transformed 10
40.0
0.0 9

10. Example blocks Random texture
Original
Transformed 11 15 18 14 13 12 16 19 17
58.8
0.3
-1.8
1.3
-3.9
-2.8
-3.5
2.6
2.7
-1.7
1.2
-3.4
3.0
-0.9
-5.3
1.8 10

11. Example blocks Impulse
Original
Transformed 10 20
42.5
1.4
-2.5
-3.2
0.7
-1.4
-1.8
2.5
3.3
4.3 11

12. Example blocks Line (horizontal)
Original
Transformed 10 20
50.0
0.0
-5.4
-10.1
13.1 12

13. Example blocks Edge (vertical)
Original
Transformed 10 20
60.0
-18.4
0.0
7.7 13

14. Example blocks Edge (horizontal)
Original
Transformed 10 20
60.0
0.0
-18.4
7.7 14

15. Example blocks Edge (diagonal)
Original
Transformed 10 20
55.0
-11.1
0.0
-0.7
5.0
4.6
-5.0
-1.9 15

16. Example blocks Slope (horizontal)
Original
Transformed 10 12 14 16
52.0
-8.9
0.0
-0.6 16

17. Quantization

18. Quantization Quantization equation: Example (q=2): Dequantization:
ci = original coefficient
q = quantization factor
Dequantization:

19. Possible quantization tables
Uniform
More accurate
Less accurate 16 1 2 4 8 16 32 64 8 64
128
256

20. Quantization tables in JPEG
Luminance (Y)
Chrominance (U,V) 16 11 10 24 40 51 61 12 14 19 26 58 60 55 13 57 69 56 17 22 29 87 80 62 18 37 68
109
103 77 35 64 81
104
113 92 49 78
121
120
101 72 95 98
112
100 99 17 18 24 47 99 21 26 66 56

21. Coding

22. Entropy coding DC coefficient AC coefficients DC coefficient:
Prediction using DC of the previous block
Prediction error by Lossless JPEG
AC coefficients:
Zig zag scanning
Subsequent zero values by run-length coding
Non-zero values by Huffman coding
Alternatively arithmetic coding
DC coefficient
AC coefficients
42.5
1.4
-2.5
-3.2
0.7
-1.4
-1.8
2.5
3.3
4.3

23. Progressive mode 1 2 3 4 Image blocks: Sequential mode DC AC AC AC …
DC DC DC DC
AC AC AC AC
AC AC AC AC
AC AC AC AC … … … …

24. Example

25. Original
139
144
149
153
155
151
156
159
150
160
163
158
161
162
157
Transformed
235.6
-1.0
-12.1
-5.2
2.1
-1.7
-2.7
1.3
-22.6
-17.5
-6.2
-3.2
-2.9
-0.1
0.4
-1.2
-10.9
-9.3
-1.6
1.5
0.2
-0.9
-0.6
-7.1
-1.9
0.9
0.0
0.3
-0.8
1.6
-0.7
0.6
1.8
-0.2
-0.3
1.0
-1.3
-0.4
-1.5
-0.5
1.7
1.1
-2.6
-3.8
-1.8
1.9
1.2

26. Quantization table Quantized 16 11 10 24 40 51 61 12 14 19 26 58 60 5513 57 69 56 17 22 29 87 80 62 18 37
109
103 77 35 64 71
104
113 92 49 78
121
120
101 72 95 98
112
100 99
Quantized 15 -1 2

27. Dequantized Reconstructed 240 -10 -24 -12 -14 -13 144 146 149 152 154
-10
-24
-12
-14
-13
Reconstructed
144
146
149
152
154
156
148
150
155
157
158
160
161
162
159
163
164

28. Visual quality
Original
JPEG 1 bpp
JPEG 0.5 bpp
JPEG bpp

29. JPEG versus PNG

30. The End