*July 2020*

tl;dr: **Self-teaching** with pseudo-label is the best way for uncertainty estimation for monocular depth estimation.

The paper has a very good review session on monocular depth estimation. Tons of ablations studies. It evaluated 11 methods and combinations for predicting the uncertainty of self-supervised monocular depth estimation.

Verdict is: When pose is known, the difference between self-teaching and log-likelihood is minor. When pose is entangled in the loss function, self-teaching is much better to produce the uncertainty of depth.

- Uncertainty by image:
**2 forward pass**- flipping: easiest one.

- Empirical estimation:
**N forward pass**- Dropout sampling: turn on random dropout during prediction
- Bootstrapped Ensemble: same model, N diff initialization
- Snapshot Ensemble: same model, N early stopped version with cyclic LR

- Predictive estimation:
**1 forward pass**- Learned reprojection: anomaly prediction predicting the
- Log-likelihood Maximization: whatever loss + aleatoric uncertainty. –> Learn SfM from SfM
**Self-teaching**: L1/L2 loss + aleatoric uncertainty

- Bayesian estimation
- Combination of empirical and predictive estimation. Uncertainty is the sum of predicted uncertainty, plus the deviation of predicted depth from the averaged depth.

- The conclusions:
- Bootstrap ensemble is about the same as snapshot ensemble, but slightly better.
- For monocular setup, empirical methods does not work well. Self-teaching improves baseline while log-likelihood worsens baseline.
- For uncertainty, self-teaching > log-likelihood > postprocessing.

- Weakly supervised:
- Noisy lidar depth
- Model-based depth: SGM for stereo, SfM, and with their confidence

- Uncertainty metric:
- Sparsification plot (see explanation in Active learning in Lidar) to compare with oracle sparsification. It is useful to compare each model with its oracle. It is usually normalized to 1 at 0 removal (max error).
- Sparsification error is the difference between each model and its oracle sparsification. It is therefore possible to compare different models. It by definition starts at [0, 0].
- The single metric summary of sparsification error is AUSE (area under the sparsification error)
- The idea was first introduced in Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow
`ECCV 2018`

- Questions and notes on how to improve/revise the current work