1. Código de Huffman

2. Código de Huffman

3. Código aritmético

4. Run-Length Encoding (RLE)

5. Codificação preditiva
• Predictive Coding
transmit the difference between
estimate of future sample &
the sample itself.
- Delta modulation
- DPCM
- Adaptive predictive coding
- Differential frame coding

6. Differential Pulse Code Modulation (DPCM)

7. Delta Modulation  + -
f (t)
y (t)
x(t)
(t)

8. Delta modulation
f(t) t
y(t)
x(t)

9. Codificação de planos de bit
a b c d e f a b c d e f

10. Codificação por transformação
• Transform Coding
- transform image
- code the coefficients of the transform
- transmit them
- reconstruct by inverse transform
• Benefits
- transform coeff. relatively uncorrelated
- energy is highly compacted
- reasonable robust relative to
channel errors

11. Padrão JPEG
"Joint Photographic Expert Group". Voted as international standard in 1992.
Works with color and grayscale images, e.g., satellite, medical, ...
Lossy and lossless

12. JPEG (intraframe)
First generation JPEG uses DCT+Run length Huffman entropy coding.
Second generation JPEG (JPEG2000) uses wavelet transform + bit plane coding + Arithmetic entropy coding.

13. Visão geral JPEG DCT (Discrete Cosine Transformation)
Quantization zigzag Scan
DPCM on DC component
RLE on AC Components
Entropy Coding

14. Porquê DCT e não DFT
DCT is similar to DFT, but can provide a better approximation with fewer coefficients
The coefficients of DCT are real valued instead of complex valued in DFT.
DCT reduces Gibbs effect between sub-image boundaries.

15. Porquê DCT e não DFT

16. DCT
Transformada discreta de cosseno
Inversa:

17. Funções base DCT de 8x8
Each 8x8 block can be looked at as a weighted sum of these basis functions.
The process of 2D DCT is also the process of finding those weights.

18. DCT

19. Quantização
F'[u, v] = round ( F[u, v] / q[u, v] ). Why? -- To reduce number of bits per sample
Example: = 45 (6 bits). q[u, v] = 4 --> Truncate to 4 bits: 1011 = 11.
Quantization error is the main source of the Lossy Compression.

20. Tabelas de quantização
Luminância
Cromaticidades
Um fator de qualidade multiplica a matriz de quantização.

21. Varredura Zig-Zag
Why? -- To group low frequency coefficients in top of vector.
Maps 8 x 8 to a 1 x 64 vector.

22. Codifica DC com DPCM
DC component is large and varied, but often close to previous value.
Encode the difference from previous 8 x 8 blocks -- DPCM

23. Codifica AC com RLE 1 x 64 vector has lots of zeros in it
Keeps skip and value, where skip is the number of zeros and value is the next non-zero component.
Send (0,0) as end-of-block sentinel value.

24. Codificação entrópica
Categorize DC values into SIZE (number of bits needed to represent) and actual bits.
Example: if DC value is 4, 3 bits are needed.
Send off SIZE as Huffman symbol, followed by actual 3 bits.
For AC components two symbols are used: Symbol_1: (skip, SIZE), Symbol_2: actual bits. Symbol_1 (skip, SIZE) is encoded using the Huffman coding, Symbol_2 is not encoded.
Huffman Tables can be custom (sent in header) or default.

25. Categorias de codificação
Size
Amplitude
-1.1 2
-3..-2,2..3 3
-7..-4,4..7 4
,8..15 5
,16..31 6
,32..63 7 , 8 , 9 , 10 ,

26. Código de luminância Categoria Tamanho Code 5 00 1 3 010 2 4 011 100 75 00 1 3
010 2 4
011
100 7
101 8
110 6 10
1110 12
11110 14
111110 9 16 18 11 20

27. Exemplo

28. JPEG 2000

29. Exemplos
Original

30. Exemplos
JPEG
27:1

31. Exemplos
JPEG2000
27:1