1. 1 STOCHASTIC SAMPLING FROM IMAGE CODER INDUCED PROBABILITY DISTRIBUTIONS regu@isis.poly.edu presenting author: memon@poly.edu viresh@google.com Google Inc., Mt. View, CA Polytechnic University, Brooklyn, NY oguleryuz@erd.epson.com Epson Palo Alto Laboratory Palo Alto, CA Regunathan Radhakrishnan, and Nasir Memon Onur G. Guleryuz, Viresh Ratnakar,

2. 2 Overview We determine the probability distributions that today’s popular, state-of-the-art coders induce on image outcomes. We consider the set of images that are well-coded by today’s popular state-of-the-art coders. We use stochastic sampling techniques to obtain typical samples from these sets. We compare typical samples to well-known images like Lena and Barbara. Are today’s coders giving us the best possible performance on natural images?

3. 3 Image Compression Systems EncoderDecoder Original Image Decoded Image Encoded bitstream E.g.: Image dimensions, Quantizer information, Marker information, … Compressed data that specifies the image pixel values.

4. 4 Image Compression Systems EncoderDecoder Original Image Decoded Image Encoded bitstream For a good image coder these bits should be random (coin tosses - i.i.d., prob(0)=prob(1)=1/2)

5. 5 This Paper Decoder Decoded Image Encoded bitstream 512x512, grayscale image, encoded at ~1 bit/pixel, … Random bits! Decoded Images shown below. (The decoding syntax will decode each data bit using a certain probability distribution. We provided random bits drawn from the appropriate distributions.)

6. 6 Background Encoder Original Image “Quantizer”Entropy Coder Introduces loss (if desired) (Same as the decoded image) image ibits U The set of all (512x512) grayscale images prob(image i) U An image coder induces a probability distribution on the image space,

7. 7 Background U Efficient set of coder U … (contains most of the induced probability) We would like to find out what the typical elements of these sets look like.

8. 8 Why? Are highly probable outcomes close to “the set of natural images”, ? N i.e., is ? If not, there is room to improve. When we are encoding Lena with coder we are spending precious bits to distinguish Lena from all the other images in. Image compression is dead. is the final word in image compression. … What kind of images is coder good for?

9. 9 How do we know … Image coders utilize data structures that allow us to talk about: JPEG: typical random blocks, SPIHT, JPEG2000: typical random trees of wavelet coefficients, JPEGLS: typical random sequences of pixels. … 1.How do we know exists? in the sense of typical sequences and Asymptotic Equipartition Theorem [1]. Coders induce typical sets that contain most of the probability. [1] T. M. Cover and J. A. Thomas, ``Elements of Information Theory.'‘ New York: Wiley, 1991. 2.How do we know we are sampling from ? The probability of not sampling from is very, …, very small.

10. 10 [3] Emmanuel Bacry, LastWave software: http://www.cmap.polytechnique.fr/~bacry/LastWave [2] S. Mallat and S. Zhong, ``Characterization of signals from multiscale edges,'' IEEE Trans. Pattern Anal. Machine Intell., vol. 14, pp. 710-732, July 1992. Conclusion Are today’s coders giving us the best possible performance on natural images? You decide. Qualitatively: Typical images are provided in this presentation. Please examine them. Quantitatively: We provide a metric that shows how important an image’s edges are in representing the image with the help of [2,3].Please ask the presenter for details and examine the results. (For natural images, edges are very important).

11. 11 SPIHT – 1 (simulations by Onur G. Guleryuz)

12. 12 SPIHT - 2

13. 13 SPIHT - 3

14. 14 SPIHT length of wavelet maxima chains starting from the finest scale

15. 15 JPEG2000 - 1 (simulations by Regunathan Radhakrishnan and Nasir Memon)

16. 16 JPEG2000 - 2

17. 17 JPEG2000 - 3

18. 18 JPEG2000

19. 19 JPEG – 1 (simulations by Viresh Ratnakar)

20. 20 JPEG - 2

21. 21 JPEG - 3

22. 22 JPEG

23. 23 JPEGLS - 1 (simulations by Regunathan Radhakrishnan and Nasir Memon)

24. 24 JPEGLS - 2

25. 25 JPEGLS - 3

26. 26 JPEGLS