*November 2019*

tl;dr: Use single-modal weighted average (SMWA) instead of full-band weighted average to reduce the over-smoothing problem in depth estimation.

Long tail is a typical problem in CNN-based depth estimation, for both monocular and disparity based, supervised or unsupervised methods. This point is echoed in pseudo lidar, pseudo lidar end to end and ForeSeE. The pseudo-lidar point with long tails confuses 3d object detectors.

DC focuses on depth completion while SMWA focuses on depth estimation from stereo pairs.

This paper seems to be heavily influenced by DC, including the soft one-hot encoding and cross entropy loss. But it did not acknowledge that.

- The proportion of pixels in a modal in all regions and the edge regions are different. The ones in edge regions are more like a bi-modal distribution.
- Single Modal Weighted Average (SWMA) in inference
- Find maximum value
- Identify the left and right range by monotonic descent
- Weighted average only in that range

- Training: Regression vs cross entropy
- Changing L1 loss on weighted averaged prediction to cross entropy with soft (gaussian smoothed, in this paper with variance of 2) one-hot label.
**CE led to superior results than L1.**

- Changing L1 loss on weighted averaged prediction to cross entropy with soft (gaussian smoothed, in this paper with variance of 2) one-hot label.
- Evaluation: soft edge error (SEE)
- For each pixel in the edge region, find the min error between the neighboring prediction and GT.
- Average all pixels in the edge region.

- 3D CNN based method:
- construct a 4D tensor based on concatenating left and right feature on location corresponding to specified disparity value, essentially adding a disparity bin dimension.
- The 4D tensor goes through 3D CNN and output d/4 x h/4 x w/4 feature map, trilinearly upsampled to full resolution d x h x w.
- Per-pixel softmax to get probability for each pixel location. Then d is weighted average of all bins.

- Minor misalignment of disparity at boundaries is acceptable as it hardly affects the local structure and over-smoothing artifact is much more desirable.
- For data set with GT depth, edge are chosen with disparity map exceeding a threshold. Otherwise we use segmentation mask, and group FG and BG classes and then dilate the boundary with 3x3 kernel.

- Need to read papers on disparity estimation, including
- In reality, over smoothing happens in many places, and typically it indicates a bimodal or multi-modal problem. It may make sense to reformulate the regression problem a classification based one.