Graph-Based Transform for 2D Piecewise Smooth Signals with Random Discontinuities
Bibliographic record
Abstract
The graph-based transform has recently emerged as an effective tool for compressing some special signals such as depth images in 3D videos. However, one limitation of this approach is that it needs to apply eigen-decomposition to each block. To reduce the complexity, in this paper, we develop a systematic approach to find a universal optimal graph-based transform for a class of 2D piecewise smooth signals. Each block in the class can include a discontinuity whose locations in different rows are randomly distributed within a confined region. We first define a special 2D graph model for this class of signals. Our derivation then reveals that the inverse of the covariance matrix of this class of signals is equal to its graph Laplacian with a bias value added to the first diagonal element. Furthermore, the edge values within the confined region have a closed-form expression. If the bias value is assumed negligible then the approximation of the optimal transform for the class of signals is given by the eigenvectors of the true graph Laplacian and can be pre-computed. Therefore online eigen-decomposition for the class of signals can be avoided, and the complexity of the encoder and decoder can thus be reduced. The feasibility of the proposed scheme is demonstrated via depth image coding examples.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".