C

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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
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Delta modulation
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Codificação de planos de bit
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Codificação por transformação
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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 DCTRun 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 ( Fu, v / qu, v ). Why? --
  To reduce number of bits per sample
• Example 101101 45 (6 bits). qu, v 4 --gt
  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 -15..-8,8..15
5 -31..-16,16..31
6 -63..-32,32..63
7 -127..-64,64..127
8 -255..-128,128..255
9 -511..-256,256..511
10 -1023..512,512..1023
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Código de luminância
Categoria Tamanho Code
0 5 00
1 3 010
2 4 011
3 5 100
4 7 101
5 8 110
6 10 1110
7 12 11110
8 14 111110
9 16 1111110
10 18 11111110
11 20 111111110
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Exemplo
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JPEG 2000
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Exemplos
Original
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Exemplos
JPEG 271
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Exemplos
JPEG2000 271