*December 2019*

tl;dr: Encode depth in a simplified one-hot encoding (DC) and cross entropy loss reduces over-smoothing in depth estimation.

#### Overall impression

Similar to the idea of SMWA to address the “long tail” problem. This problem can be also referred to as edge bleeding, over-smoothing, or mixed depth. It features spurious depth estimation in mid-air and connecting surfaces between separate objects.

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

It also acknowledges that the problem is a multi-modal problem and using L1 or L2 leads to spurious estimation in-between modes. –> this is also used in generalized focal loss to model multi-modal distribution of edges of heavily occluded objects.

The idea of using an N-channel but 3-hot depth encoding is similar to the soft one-hot encoding used in SMWA. In SMWA it also uses cross entropy for regression. DC gives a better explanation why cross entropy is a better loss than L1 or L2.

The input and loss modification is based on sparse-to-dense and is easy to implement.

#### Key ideas

- One-hot encoding of depth and the use of cross-entropy loss solves the problem of mixed-depth problem.
- direct one-hot encoding may leads to too sparse depth samples, and thus intentional information leaking by (gaussian) blurring across depth direction increases samples for convolution.

- Cross entropy loss for depth bin j and pixel i. For each pixel i, only 3 pixels are with non-zero $c_{ij}$. This is similar to the idea of nll loss used in depth from one line.
\(L^{ce}(c_{ij}) = -\sum_{j=1}^N c_{ij}\log\tilde{c_{ij}}\)
**RMSE favors over-smoothed depth estimation and thus is not a reliable metric.**

#### Technical details

- Depth reconstruction: either weighted average, or pick the single modal weighted average (eq 7). –> However the paper did not go to details on this.
**The output dense depth leads to improved lidar performance**. –> this is to be compared with pseudo lidar e2e which suffers from long tail problem.

#### Notes

- But after thinking about this again: how does changing the one-hot encoding into soft one-hot encoding help in alleviating the problem? How does cross entropy come to rescue when N degenerates to 1? Then it becomes softmax loss. –> cross entropy enables multi-modal?