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Learning Triangular Distribution in Visual World
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Proposes Triangular Distribution Transform (TDT), a parameter-free plug-in that maps feature differences linearly to label differences for label distribution learning, evaluated on facial age, aesthetics, and illumination estimation.
Problem
Label distribution learning with CNNs maps nonlinear visual features to labels without a guaranteed correspondence between feature discrepancy and label discrepancy, so the feature-to-label mapping is ambiguous and not guaranteed to be correct.
Approach
A parameter-free Triangular Distribution Transform converts feature statistics into symmetric triangular-distribution feature differences so that a linear head can map them to label differences, trained with symmetry, commutativity and supervised comparative losses using prior-sample comparisons.
Key results
- On MegaAge-Asian, TDT reaches CA(3) 69.60 vs. DAA 68.82, CA(5) 85.42, CA(7) 93.26.
- On FG-Net, TDT achieves MAE 2.12, the lowest among compared methods (PML 2.16, DAA 2.19).
- On TAD66K, TDT achieves MSE 0.0172, second best behind TANet (0.0161) and better than SAAN (0.0185).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| replace DAA mapping with TDT | DAA · MegaAge-Asian | CA(3): 68.82 -> 69.60 | Helped |
| replace DAA mapping with TDT | DAA · FG-Net | MAE: 2.19 -> 2.12 | Helped |
| replace SAAN head with TDT | SAAN · TAD66K | MSE: 0.0185 -> 0.0172 | Helped |
| add TDT to FC4 with sRGB data | FC4+sRGB · Color Checker | mean angular error: 1.51 -> 1.46 | Helped |
| add symmetry-related loss LS (ablation) | TDT · MegaAge-Asian | CA(3): 67.74 -> 69.60 | Helped |
| add commutativity-related loss LM (ablation) | TDT · MegaAge-Asian | CA(3): 68.43 -> 69.60 | Helped |
| add symmetry-related and commutativity-related losses (ablation) | TDT · MegaAge-Asian | CA(3): 68.26 -> 69.60 | Helped |
| use unlabeled losses on all data rather than part2 only (ablation) | TDT · MegaAge-Asian | CA(3): 66.59 -> 69.60 | Helped |
| increase feature distributions from 32 to 128 (ablation) | TDT · MegaAge-Asian | CA(3): 67.80 -> 69.60 | Helped |
| increase prior samples from 64 to 256 (ablation) | TDT · MegaAge-Asian | CA(3): 67.34 -> 69.60 | Helped |
Surprising findings
- On Color Checker, TDT+FC4 has higher mean and median angular error than several prior methods (e.g., IGTN, MDLCC), so gains are not uniform across metrics.
- Removing the symmetry loss hurts less than expected? No: the paper reports symmetry loss gives the largest improvement, while using 128 feature distributions was optimal rather than more.
Limitations
- Relies on a prior sample set for comparisons, adding design choices (prior set size and selection).
- Results on illumination estimation are mixed; TDT+FC4 underperforms several methods on mean and median error without sRGB data.
- Triangular approximation is justified by method of moments and the linearity assumption is asserted rather than proven for all tasks.
Experimental setup
Datasets: FG-Net MegaAge-Asian TAD66K Reprocessed Color Checker
Benchmarks: FG-Net MegaAge-Asian TAD66K Reprocessed Color Checker
Metrics: MAE cumulative accuracy MSE recovery angular error
Baselines: DAA PVP LRN SSR-Net PML TANet SAAN FC4 MDLCC TLCC+sRGB FFCC
Builds on: DAA FC4 SAAN label distribution learning
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