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STOCHASTIC SAMPLING FROM IMAGE CODER INDUCED PROBABILITY DISTRIBUTIONS

STOCHASTIC SAMPLING FROM IMAGE CODER INDUCED PROBABILITY DISTRIBUTIONS. presenting author:. Onur G. Guleryuz, Viresh Ratnakar,. oguleryuz@erd.epson.com Epson Palo Alto Laboratory Palo Alto, CA. viresh@google.com Google Inc., Mt. View, CA. Regunathan Radhakrishnan, and Nasir Memon.

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STOCHASTIC SAMPLING FROM IMAGE CODER INDUCED PROBABILITY DISTRIBUTIONS

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

  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. Image Compression Systems Decoded Image Original Image Encoder Decoder Encoded bitstream < format bits > < data bits > < format bits > < data bits > < … > E.g.: Image dimensions, Quantizer information, Marker information, Compressed data that specifies the image pixel values. …

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

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

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

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

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

  9. How do we know … • How do we know exists? 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. … in the sense of typical sequences and Asymptotic Equipartition Theorem [1]. Coders induce typical sets that contain most of the probability. • How do we know we are sampling from ? The probability of not sampling from is very, …, very small. [1] T. M. Cover and J. A. Thomas, ``Elements of Information Theory.'‘ New York: Wiley, 1991.

  10. 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). [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. [3] Emmanuel Bacry, LastWave software: http://www.cmap.polytechnique.fr/~bacry/LastWave

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

  12. SPIHT - 2

  13. SPIHT - 3

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

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

  16. JPEG2000 - 2

  17. JPEG2000 - 3

  18. JPEG2000

  19. JPEG – 1 (simulations by Viresh Ratnakar)

  20. JPEG - 2

  21. JPEG - 3

  22. JPEG

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

  24. JPEGLS - 2

  25. JPEGLS - 3

  26. JPEGLS

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