8icom - 8 Image Compression Chapter 8(Image Compression...

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8. Image Compression Chapter 8 (Image Compression)
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Image and Video Coding Coding: Source Coding (e.g. compression) & Channel Coding (e.g. error correction coding) Typical Image /Video Storage/Transfer environments: Source Coding Channel Coding Source Decoding Channel Decoding Channel and/or Storage Image/Video Reconstructed Image/Video Source Coding: Lossless or Lossy . Image/video compression standards use a combination of Lossy and Lossless compression algorithms.
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Lossless compression - also called entropy coding, reversible coding. Lossy compression , but can be very close - also called irreversible coding Compression ratio: (Number of bits in X)/(Number of bits in ) Encoder Decoder Original X Compression Compressed Y Decompressed (or Reconstructed) ˆ XX ˆ ˆ X Y
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Lossless Coding Run-length coding, Huffman coding, Arithmetic coding, … Lossless compression algorithms are often used for compressing medical or business documents (for legal reasons).
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Elements of Information Theory The set of source symbols, , with event occurrence probability Self Information:   a a a J , , , 2 1   . ) ( a j P z )) ( ( log ) ) ( 1 ( log ) ( 2 2 a a a j j j P P I (bits)
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Elements of Information Theory Entropy (uncertainty): amount of information associated with a set of source symbols. )) ( ( log ) ( ) ( 2 1 a a j J j j P P z H ( in bits/symbol, representing the minimum number of bits to represent the source symbols )
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Huffman Coding 1.0 1.0 0.4 0.4 0.3 0.3 0.2 0.2 0.6 0.6 0.1 0.1 0.2 0.2 b 0.2 0.2 f 0.1 0.1 c 0.1 0.1 g 0.05 0.05 a 0.05 0.05 d 0.3 0.3 e 0 1 0 0 1 1 1 1 1 0 0 0 Entropy: 2.546439 bits/symbol Entropy: 2.546439 bits/symbol Average coding rate: 2.6 bits/symbol Average coding rate: 2.6 bits/symbol 0.05 5 0.2 2 0.1 3 ii lp  • Not unique Not unique
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Variations of Huffman Coding For practical reasons, some variations of Huffman coding are used. Truncated Huffman code: the last m+1 symbols (assuming all symbols have been ordered based on prob.) are coded with fixed-length codes with a special prefix. The “ prefix symbol ” should have the prob. equal to the sum of prob. from , and is coded with the first m symbols by the Huffman procedure. a a J m 1
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decaf (5 symbols) 10100111001010100 Error propagation: 10 0 00111001010100 cfecaf (6 symbols) Error Propagation • Data expansion
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Arithmetic Coding S i p i Sub-interval a 0.1 [0.0, 0.1) b 0.2 [0.1, 0.3) c 0.1 [0.3, 0.4) d 0.1 [0.4, 0.5) e 0.3 [0.5, 0.8) f 0.15 [0.8, 0.95) # 0.05 [0.95, 1.0) 0.459285 = 0.01110101100100111011… 0.459283 = 0.01110101100100111001… Send 0.0111010110010011101 = 0.45928387…
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Arithmetic Coding
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8icom - 8 Image Compression Chapter 8(Image Compression...

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