The JPEG Still Picture Compression Standard

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The JPEG Still Picture Compression Standard

• Gregory K. Wallace
• (presentation by Scott Dexter)

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Overview
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Purpose and Requirements

• Effective compression for still images across
  variety of domains
• Standardization
• (Note this was before the Web, 1988-1990)
• State-of-the-art compression ratio and image
  fidelity (esp for high-fidelity images)
• Applicable to any kind of digital image
• Tractable complexity
• Supportive of several modes of operation

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Operating Modes

• Standard provides many possibilities a given
  application only needs to implement what is
  necessary
• Sequential image compressed through a single
  L-R, top-bottom scan (Baseline)
• Progressive Image processed in several scans of
  increasing fidelity (for slow/long transmission)
• Lossless recovered image is exact duplicate of
  original (much less compression)
• Hierarchical compressed at multiple resolutions
  that can be accessed independently

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Baseline DCT Coding

• Compression of a stream of 8x8 grayscale samples
• (Color images are multiple grayscale images)
• Each 8x8 sample is shifted from 0,255 to
  -128,127 in preparation for DCT
• DCT converts spatial information into spatial
  frequencies
• Output is coefficients of 64 orthogonal basis
  signals (see images of these signals from
  earlier DCT presentation)

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Baseline DCT Coding

• DCT frequency representation allows exact
  recovery of original image (except for
  imperfections of computation)
• Despite sensitivity to computation, JPEG does not
  specify particular DCT/inverse algorithms.
• But because most images change slowly across
  space, most energy concentrated in low
  frequencies
• Zero-frequency coefficient is DC others are
  AC

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Baseline Quantization

• Each of the 64 coefficients is then quantized by
  comparison with a 64-element Quantization Table
  (which can be defined by user/app)
• Each element of QT is integer 1-255, which
  specifies size of quantizer for corresponding
  coefficient.
• Quantization
• Recovery

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Baseline Quantization

• To compress without visual artifacts,
  quantization step chosen as the just noticeable
  difference for contribution of basis function
• JPEG standard includes recommended (but not
  required) QTs for various situations/applications

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Baseline Entropy Coding

• DC and AC coefficients treated separately
• Each DC coefficient represented as difference
  from previous DC coefficent
• AC coefficients put in zig-zag list to put all
  low-frequency (likely non-zero) coefficients
  before high-frequency
• Then AC coefficients compressed (losslessly)
  using Huffman or arithmetic coding
• Huffman can be based on predefined tables or on
  image statistics
• Arithmetic requires no extra tables, but viewed
  by some as more complex

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Baseline Entropy Coding

• Two steps
• First convert zig-zag sequence into sequence of
  intermediate symbols
• Then convert symbol sequence into stream of bits
• Intermediate representation
• Two types of symbols symbol-1 and symbol-2
• AC and DC coefficients handled differently
• AC coefficients often in pattern of many zeroes
  followed non-zero
• Each coefficient represented as symbol-1
  (RUNLENGTH,SIZE) followed by symbol-2 AMPLITUDE
• RUNLENGTH is number of zeros SIZE is number of
  bits to represent AMPLITUDE (DCT values require
  at most 3 more bits than pixel values)
• RUNLENGTH is 0 to 15 SIZE is 1 to 10

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Baseline Entropy Coding

• DC coefficients symbol-1 is SIZE symbol-2 is
  AMPLITUDE
• remember DC values are represented as
  differences need extra bit compared to
  magnitudes of AC values
• SIZE is number of bits to represent AMPLITUDE 1
  to 11
• Symbol-2 values are stored as variable-length
  integers
• Length given by preceding symbol-1 value
• Precise representations of values hardcoded in
  JPEG standard
• Not entropy-optimal, but pretty close, and more
  efficient
• Symbol-1 values are stored as variable-length
  Huffman codes (from tables or pre-processing)

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Compression vs Quality

• 1.5-2.0 bits/pixel indistinguishable from
  original
• 0.75-1.5 bits/pixel excellent
• 0.5-0.75 bits/pixel good to very good
• 0.25-0.5 bits/pixel moderate quality

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Lossless Coding

• Some applications cant deal with loss of image
  information (eg medical)
• JPEG provides a simple predictive coding method
  that gives about 50 compression
• Idea compute a predicted value for pixel (x,y)
  based on values of (x-1,y), (y-1,x), and
  (x-1,y-1)
• Prediction will be close but (usually) wrong
• Store the difference
• Encode the differences using entropy coding