On Rate-Distortion Models for Natural Images and Wavelet Coding Performance
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Bibliographic record
Abstract
Operational rate-distortion (RD) functions of most natural images, when compressed with state-of-the-art wavelet coders, exhibit a power-law behavior D alpha R(-gamma) at moderately high rates, with gamma being a constant depending on the input image, deviating from the well-known exponential form of the RD function D alpha 2(-xiR) for bandlimited stationary processes. This paper explains this intriguing observation by investigating theoretical and operational RD behavior of natural images. We take as our source model the fractional Brownian motion (fBm), which is often used to model nonstationary behaviors in natural images. We first establish that the theoretical RD function of the fBm process (both in 1-D and 2-D) indeed follows a power law. Then we derive operational RD function of the fBm process when wavelet encoded based on water-filling principle. Interestingly, both the operational and theoretical RD functions behave as D alpha R(-gamma). For natural images, the values of gamma are found to be distributed around 1. These results lend an information theoretical support to the merit of multiresolution wavelet compression of self-similar processes and, in particular, natural images that can be modelled by such processes. They may also prove useful in predicting performance of RD optimized image coders.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.002 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it