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Código de Huffman

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Código de Huffman

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Código aritmético

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**Run-Length Encoding (RLE)**

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**Codificação preditiva**

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

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**Differential Pulse Code Modulation (DPCM)**

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Delta Modulation + - f (t) y (t) x(t) (t)

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

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**Codificação de planos de bit**

a b c d e f a b c d e f

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**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

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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

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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.

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**Visão geral JPEG DCT (Discrete Cosine Transformation)**

Quantization zigzag Scan DPCM on DC component RLE on AC Components Entropy Coding

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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.

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Porquê DCT e não DFT

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DCT Transformada discreta de cosseno Inversa:

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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.

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DCT

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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.

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**Tabelas de quantização**

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

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

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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

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**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.

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**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.

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**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 ,

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**Código de luminância Categoria Tamanho Code 5 00 1 3 010 2 4 011 100 7**

5 00 1 3 010 2 4 011 100 7 101 8 110 6 10 1110 12 11110 14 111110 9 16 18 11 20

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Exemplo

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JPEG 2000

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Exemplos Original

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Exemplos JPEG 27:1

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Exemplos JPEG2000 27:1

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Klara Nahrstedt Spring 2011

Klara Nahrstedt Spring 2011

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