Tuesday, March 15th, 2005
Eero Simoncelli’s “Statistical Modeling of Photographic Images”
Main idea:
Out of the huge set of possible images, a particular subset of likely images exist, and these images can be described using a probability model.
Three probability models are discussed:
- The Gaussian Model
- pros
- easy computations
- single parameter
- direct application to compression and noise removal
- cons
- unconstrained phase (can destroy image content)
- doesn’t capture structure in most real images
- pros
- The Wavelet Marginal Model
- pros
- captures non-gaussian histogram characteristics (with peaks at zero and long tails)
- better fit (reduced entropy) leads to improved compression and noise removal
- cons
- important image information is still not captured
- wavelet coefficients are not independent — their high-order statistics are correlated
- pros
- Wavelet Joint Models
- pros
- adapts to local variance
- gaussian scale mixture (GSM) model is useful
- gives much improved noise removal results
- cons
- still can’t capture all image structure
- pros
