Compression I

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Compression (I)

• RPI ECSE DocLab
• Jie Zou

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Compression is complicated!

• Why so many algorithms?
• Source coding / channel coding
• Storage / Transmission
• Lossy / Lossless compression
• Visual files / General binary or ASCII files
• Image / Video
• Document image / Natural image / Graphics
• We discuss only source coding, and mainly on
  document and natural image compression.

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Typical Environment for Image Coding
Transmitter
Source encoder
Channel encoder
Image Source
Channel
Receiver
Channel decoder
Source decoder
Recovered image
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Todays topics

• Lossless compression algorithm
• Run Length Coding (RLC)
• Huffman coding
• Dictionary based methods (LZW)
• Lossy compression standards
• JPEG / JPEG2000
• MPEG-1, -2, -4

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Run Length Coding (RLC)

• Utilize the repetition of characters.
• Mostly used for binary pictures (document
  images)
• Examples
• 0001111100111 ? 3523
• 0011100011101 ? 233311
• 101000000000 ? 01119

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Dictionary Based Method

• Principle replacing substrings with a codeword
  that identifies that substring in a dictionary.
• All adaptive dictionary methods are based on the
  method proposed by Ziv and Lempel in 70.
• LZ77, LZ78, LZW

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LZ77

• Codeword is a triple.
• How far back to look
• How long the phase is
• The next char from input
• Example
• Gzip (variant of LZ77)

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LZ78

• Codeword is a pair
• String number
• The next char from input
• Example
• LZW (variant of LZ78)
• More widely known and very interesting
• Used in UNIX compress command, and GIF

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LZW encoder

• 1 Initialize string table
• 2 Prefix C ? empty
• 3 K ? next character in charstream
• 4 Is CK in string table?
• (Yes C ? CK)
• (No add CK to the string table
• output the code for C to the codestream
• C ? K)
• 5 Goto 3

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LZW decoder

• 1 Initialize string table
• 2 Get first code ltcodegt
• 3 Output the string for ltcodegt to the
  charstream
• 4 ltoldgt ltcodegt
• 5 ltcodegt ? next code in codestream
• 6 Is ltcodegt in the string table?
• (Yes output the string for ltcodegt to the
  charstream
• ? translation of ltoldgt
• K ? first character of translation for ltcodegt
• add K to the string table)
• (No ? translation for ltoldgt
• K ? first character of
• output K to charstream and add it to string
  table)
• 7 ltoldgt ? ltcodegt
• 8 Goto 5

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Entropy

• Entropy can be interpreted as the average amount
  of information that a message contains.
• Entropy is the theoretically minimum possible
  average bit rate required in coding a message.

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Huffman Coding

• Shorter bits for more frequently appeared
  messages and longer bits for less frequently
  appeared messages.
• Example 1.
• Huffman coding is near optimal, but in general
  the average bits can not be as low as entropy.
• Example 2.

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Compression Standards

• Bilevel images (documents, FAX)
• CCITT G3, G4, JBIG, JBIG2 (Prof. Nagy will
  discuss them.)
• Grayscale and color still images
• JPEG (Joint Photographic Experts Group)
• JPEG2000
• Video
• CCITT H.261, ITU-T H.320 and H.324, CCIR721 and
  723.
• MPEG 1, 2, 4 (Moving Picture Experts Group ).

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Baseline JPEG
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Zigzag Scanning
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MPEG Technique Overview Video Basics

• I Frame, P Frame and B Frame
• I Frame Intra Frame (similar to JPEG)
• P Frame forward Predict future Frame
• B Frame Bi-directional interpolated prediction
  frames
• Motion Estimation
• Basic premise most change due to movement
• Coding only Residual Errors