Código de Huffman

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

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

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

10. • 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 Codificação por transformação

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: 101101 = 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

26. Código de luminância

27. Exemplo

28. JPEG 2000

29. Exemplos Original

30. Exemplos JPEG 27:1

31. Exemplos JPEG2000 27:1