1. JPEG-LS -- The new standard of lossless image compression
School of Computer Science,
University of Central Florida,
VLSI and M-5 Research Group
May, 1999

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

3. Predictive encoding
Lossless JPEG
JPEG-LS
CALIC ……

4. What’s wrong with Lossless JPEG ?C B A X
Lossless JPEG uses “static” predictor. The prediction model is determined before the compression starts

5. JPEG-LS is better because…
“Dynamic” predictor. The predictor is determined dynamically
Simple edge detection algorithm is introduced to determine the predictor.
Prediction refinement

6. JPEG-LS: initial predictionc b d a X
Prediction algorithm:
If c  max(a, b)
X^ = min(a, b)
Else {
If c  min(a, b)
X^ = max(a, b)
X^= a + b- c }
X is the pixel being encoded
a, b and c used for initial prediction

7. JPEG-LS: initial prediction example
103
100 d 99
100 d
102 X
102 X
X is predicted as 100 since a vertical edge is detected
X is predicted as 102 since a horizontal edge is detected

8. 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 predictor’s performance for that particular context.
The bias is used for refinement of the initial prediction
X’’ = X’ – B[q]
where X’ is the initial prediction, X’’ is the refined prediction, q is the context of X and B is the bias

9. JPEG-LS: prediction refinement example
103
100 d
102 X
X’ = 100
Suppose X is in context q and B[q] = -1, then X’’ = 100 – (-1) = 101

10. JPEG-LS: compute the prediction error, update the bias
Compute the prediction error as:
Prediction Error = X – X’’
Update the context-dependent bias

11. Ready for entropy encoding? Wait……

12. 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’’]

13. JPEG-LS: Re-map residuals
The following example assumes pixel value is in [0, 7] -3 -2 -1 1 2 3 4 6 5 7
Mistake in David Salomon’s book?
X’’’ = 2x’’ if x’’>=0
X’’’ = 2|x’’|-1 otherwise -3 -2 -1 1 2 3 4 5 6 8

14. JPEG-LS: entropy encoding
Finally entropy encoder is applied.

15. 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