1. IMPROVING THE PERFORMANCE OF JPEG-LS Michael Syme 18171613 Supervisor: Dr. Peter Tischer

2. 2 Introduction Terms: Lossy Compression: Loss of data; Loss in image quality. Lossless Compression: No loss of data; No loss in image quality. Near Lossless Compression: Loss of data up to a predetermined amount (Pd) at each pixel value. Eg: No pixel value can change by more than ‘t’.

3. 3 Introduction Cont’d LOCO-I (Low Complexity Lossless Compression of Images) is the algorithm at the heart of JPEG-LS. JPEG-LS was introduced as a standard in 1999 for lossless compression. Achieves good compression and high throughput for a low complexity algorithm. However, JPEG-LS is not optimal. Therefore, it can be improved!

4. 4 JPEG-LS Description Terms: Predicted Value: JPEG-LS predicts the current pixel value by making an estimation from its neighbouring pixels. Prediction Error: After some internal adjustments of the predicted value, the prediction error is calculated and encoded. It is important that the prediction error is small.

5. 5 JPEG-LS Description Cont’d Terms: Causal Neighbourhood: Neighbourhood of pixels surrounding the current pixel. Common Knowledge: Previous pixel values which both the encoder and decoder know.

6. 6 Coding Terms: Flat Region: When the pixels surrounding the current pixel, are equal or less than a predetermined amount. Gradients: d1 = d – a; d2 = a – c; d3 = c – b; Flat region: d1,d2,d3 <= Pd

7. 7 Past Research Research has focused on improving the detection of edges. However, this does not guarantee an improvement in compression amounts. Another area is rate-controlled region of interest coded images. However, this raises the question of how much extra information is needed to encode the region of interest. No research has considered the affects of noisy images on quantisation error values.

8. 8 JPEG-LS Limitations Coding and Compression: Golomb Encoder must output at least 1 bit-per-pixel. Predictor: Large quantisation errors act similarly to noise. Also, the median predictor used is inefficient in the presence of noise. Coding for region of interest: Currently, the JPEG- LS standard is unable to code for regions of interest. Therefore, its functionality is limited.

9. 9 Methods, Results and Discussion

10. 10

11. 11

12. 12 1. Coding and Compression

13. 13 Coding Solution A Run Length Coder detects and specially encodes repetitive bits and long streams of 0’s and 1’s. A Whitening Transform procedure detects repeating bit stream patterns of 1’s and 0’s. It converts the compressed file into long streams of 0’s and 1’s, which a RLC can then encode.

14. 14 Run Length Coder (RLC) Image from CSE457 (Data and Image Compression) Assignment 1 by Dr. Peter Tischer

15. 15 RLC Cont’d Threshold Value: number of repeating 1’s or 0’s to trigger the run mode. If the threshold value is 3, then three 1’s or three 0’s are output, followed by the leading and trailing bits. Leading calculations: leading = floor(log2(integer)) + 1; Trailing calculations: trailing = integer & (~(1 << leading-1));

16. 16 Implied Terminating Bit: The bit of the opposite sign, which terminates a run. For example 11110  0 is the terminating bit. Implied Bit: a run of 1’s is terminated by a 0 bit, or the end of file. Therefore, we can assume the occurrence of the terminating bit unless an end of file is reached. This allows us to save 1 bit each time. Note: We save one bit per run length and not one bit each time.

17. 17 Coding and Compression Results Implied B-O RLC performed better then the Original B-O RLC. This was expected since we are saving a bit on each run. Images with low amounts of edges, are highly predictable, and could be further compressed by B-O RLC. This proves the limitations of Golomb-Rice Coder. Images that are unpredictable (i.e. contain a large amount of edges) could not be compressed as much as predictable images. The gain or increase in compression decreases as the degree of loss increases.

18. 18 Coding and Compression Results Cont’d Implied LosslessFrance DISFrance EN 32.036791.35112 42.060051.35148 82.142311.38165 122.237021.43112 162.19821.41004 242.20311.41127 322.202521.41107 Orig2.202551.4111

19. 19 Coding and Compression Results (RLC & Whitening Transformation) Implied EN LosslessFranceFrance W4France W8France W12France W16 31.351121.344931.321071.294691.01781 41.351481.346411.325941.299561.00379 81.381651.37491.356731.341491.01044 121.431121.425091.40861.397321.03079 161.410041.405481.39051.382031.04793 241.411271.407211.395831.391131.07414 321.411071.408531.400151.397491.09596 Orig1.4111

20. 20 2. Improving Prediction in the Presence of Noise

21. 21 Predictor Solution Substituting the median predictor with the following predictors: 1. Average Four = (A + B + C + D) / 4; 2. West = A; 3. North = B; 4. North West = C; 5. Mean = (A + B) / 2; 6. Pirsch = A / 2 + (B + D) / 4; 7. Plane = A + B – C;

22. 22 Predictor Results The median predictors works poorly as the degree of loss increases. The increase in degree of loss, causes an increase in quantisation errors, which begin to act as noise. Best performing predictors are Pirsch and Average 4. This was expected as the two predictors are more tolerant of noise than the median predictor.

23. 23 Predictor Results Cont’d Loss 12LennaCLena NoiseMandrillCFranceBarb Aver41.12492.09411.87060.51141.1156 Mean1.13662.12981.86110.50421.1211 Median1.15762.21711.87650.49941.1126 North1.14262.12961.91770.51781.1044 NorthWest1.16782.15861.91150.54491.1748 Pirsch1.12912.11341.85510.50691.1221 Plane1.18132.33881.91350.51051.1484 West1.19542.21361.88170.51261.1902 % Incr2.82825.54561.13830.00000.7325

24. 24 3. Region of Interest Coding

25. 25 Region of Interest Coding Questions How do you tell the decoder where the region of interest is? How much information is needed in order to code the regions of interest? How much change or reconstruction of the JPEG-LS standard is needed, in order to include this functionality? How do we store the information if JPEG-LS encoding /decoding is heavily dependant on previously encoded/decoded information?

26. 26 Region of Interest Coding Solution Near-Lossless Map: A 2-dimensional array containing the degrees of loss (i.e. near lossless values) for each pixel within an image. How do we include this extra information? 0 loss corresponds to lossless encoding (i.e. region of interest) 222222 221122 210012 210012 221122 222222

27. 27 Region of Interest Coding Solution Method One JPEG-LS allows for multi band coding techniques. For example, A coloured image can be encoded by rows of red, green and blue.

28. 28 Region of Interest Coding Solution Method Two Another method is to encode the near-lossless map before the encoded image data.

29. 29 Region of Interest Coding Solution Cont’d JPEG-LS does not allow for multiple degrees of loss to be used at once. JPEG-LS must be changed to allow for different encoding of regions Large number of variables are dependant on the near lossless value. Therefore, all dependant variables must be replicated for each different degree of loss, and should only be used when their associated near value is used.

30. 30 Conclusion

31. 31 Conclusion Compress JPEG-LS encoded images by post process operations. Improve prediction in the presence of noise and large degrees of loss. Improve the functionality of JPEG-LS to include region of interest coding.

32. 32 Future Work A different RLC may be used to represent a repeated run. A combination of several predictors would give the optimal compression for the standard. Implementation of region of interest coding for JPEG-LS. This would be useful for image oriented industries such as medicine, image processing, etc…

33. 33 Conclusion Cont’d My website: http://www.csse.monash.edu.au/~msyme A public domain/ open source JPEG-LS coder can be found at: http://www.hpl.hp.com/loco/software.htm Further information about JPEG-LS can be found at: http://www.hpl.hp.com/loco/indexold.htm A viewer of JPEG-LS files can be downloaded from Pegasus at: http://www.pegasusimaging.com/jpegls.htm