JPEG-LS -- The new standard of lossless image compression

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JPEG-LS-- The new standard of lossless image
compression

• School of Computer Science,
• University of Central Florida,
• VLSI and M-5 Research Group

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Predictive encoding

• Q why prediction?
• A to produce a more skewed set of sequence for
  entropy encoder

Original sequence 20 21 125 126 30 31 32
Prediction errors 20 1 104 1 -96 1 1
Prediction example
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Predictive encoding

• Lossless JPEG
• JPEG-LS
• CALIC

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Whats wrong with Lossless JPEG ?

• Lossless JPEG uses static predictor. The
  prediction model is determined before the
  compression starts

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JPEG-LS is better because

• Dynamic predictor. The predictor is determined
  dynamically
• Simple edge detection algorithm is introduced to
  determine the predictor.
• Prediction refinement

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JPEG-LS initial prediction
Prediction algorithm

• If c ? max(a, b)
• X min(a, b)
• Else
• If c ? min(a, b)
• X max(a, b)
• Else
• X a b- c

• X is the pixel being encoded
• a, b and c used for initial prediction

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JPEG-LS initial prediction example

• X is predicted as 100 since a vertical edge is
  detected

• X is predicted as 102 since a horizontal edge is
  detected

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JPEG-LS refine the prediction

• JPEG-LS maintains 365 contexts. it is used to
  describe the local characteristics of pixels.
• Context of X is computed from a, b and d
• Each context maintains a bias, which can be
  considered as an evaluation of the predictors
  performance for that particular context.
• The bias is used for refinement of the initial
  prediction
• X X Bq
• where X is the initial prediction, X is the
  refined prediction, q is the context of X and B
  is the bias

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JPEG-LS prediction refinement example

• X 100
• Suppose X is in context q and Bq -1, then X
  100 (-1) 101

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JPEG-LS compute the prediction error, update the
bias

• Compute the prediction error as
• Prediction Error X X
• Update the context-dependent bias

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Ready for entropy encoding? Wait
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JPEG-LS Re-mapping example

• If the pixel value is in range 0, 255, the
  prediction error is in range -255, 255
• A larger range means more bits to represent the
  prediction error
• We need to re-map the prediction errors to 0,
  255, is it possible?
• Yes. Since the prediction error always in range
  -x, 255-x

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JPEG-LS Re-map residuals
The following example assumes pixel value is in
0, 7
-3 -2 -1 0 1 2 3 4
6 4 2 0 1 3 5 7
Mistake in David Salomons book? X 2x if
xgt0 X 2x-1 otherwise
-3 -2 -1 0 1 2 3 4
5 3 1 0 2 4 6 8
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JPEG-LS entropy encoding

• Finally entropy encoder is applied.

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Summary of the basic steps of JPEG-LS

• Find the initial prediction X
• Refine prediction by considering the bias of the
  context
• Compute the prediction error (residual) and
  update the bias of that context
• Re-map residuals
• Encode residuals using Golomb-Rice coder