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STOCHASTIC SAMPLING FROM IMAGE CODER
INDUCED PROBABILITY DISTRIBUTIONS
presenting author:
[email protected] Inc., Mt. View, CA
Polytechnic University, Brooklyn, NY
[email protected] Palo Alto Laboratory
Palo Alto, CA
Regunathan Radhakrishnan, and Nasir Memon
Onur G. Guleryuz, Viresh Ratnakar,
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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?
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Image Compression Systems
Encoder Decoder
Original Image
Decoded Image
Encoded bitstream
< format bits > < data bits > < data bits >< format bits > < … >
E.g.:Image dimensions,Quantizer information,Marker information,…
Compressed data that specifies the imagepixel values.
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Image Compression Systems
Encoder Decoder
Original Image
Decoded Image
Encoded bitstream
< format bits > < data bits > < data bits >< format bits > < … >
For a good image coder these bits should be random
(coin tosses - i.i.d., prob(0)=prob(1)=1/2)
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This Paper
Decoder
Decoded ImageEncoded bitstream
< format bits > < data bits > < … >
512x512, grayscaleimage, 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.)
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Background
Encoder
Original Image
“Quantizer” Entropy Coder
Introduces loss (if desired)
(Same as the decoded image)
image i il bits
U
The set of all (512x512) grayscale images
il2~prob(image i)
UAn image coder induces a probability distribution on the image space,
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BackgroundU
,1C UE( )1CEfficient set of coder
U
,2C UE( )2CEfficient set of coder
…
(contains most of the induced probability)
•We would like to find out what the typical elements of these sets look like.
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Why?
•Are highly probable outcomes close to “the set of natural images”, ?Ni.e., is ?NE( ~)iC
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 .
,iC)iCE(
Image compression is dead.< Insert coder here > is the final word in image compression.
…
•What kind of images is coder good for?iC
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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.…
)iCE(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 ?)iCE(The probability of not sampling from is very, …, very small.)iCE(
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).
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SPIHT – 1 (simulations by Onur G. Guleryuz)
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SPIHT - 2
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SPIHT - 3
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SPIHT
length of wavelet maxima chains starting from the finest scale
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JPEG2000 - 1 (simulations by Regunathan Radhakrishnan and Nasir Memon)
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JPEG2000 - 2
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JPEG2000 - 3
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JPEG2000
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JPEG – 1 (simulations by Viresh Ratnakar)
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JPEG - 2
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JPEG - 3
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JPEG
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JPEGLS - 1 (simulations by Regunathan Radhakrishnan and Nasir Memon)
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JPEGLS - 2
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JPEGLS - 3
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JPEGLS