# zhu_unsupervised_2018: Unsupervised Event-based Learning of Optical Flow, Depth, and Egomotion

## Unsupervised Event-based Learning of Optical Flow, Depth, and Egomotion

### Contributions

The authors propose a new input representation that captures the spatiotemporal distribution of events, and a set of unsupervised loss functions that allows for learning of motion information only from the event stream.

### Input Representation

Given a set of $$N$$ input events $$\left\{\left(x_{i}, y_{i}, t_{i}, p_{i}\right)\right\}_{i \in\left[1, \infty^{n}\right.}$$, and a set of $$B$$ bins to discretize the time dimension, the timestamps are scaled to the range $$[0, B-1]$$, and the event volume is generated as:

\begin{aligned} t_{i}^{*} &=(B-1)\left(t_{i}-t_{0}\right) /\left(t_{N}-t_{1}\right) \\\
V(x, y, t) &=\sum_{i} p_{i} k_{b}\left(x-x_{i}\right) k_{b}\left(y-y_{i}\right) k_{b}\left(t-t_{i}^{*}\right) \\\
k_{b}(a) &=\max (0,1-|a|) \end{aligned}

where $$k_{b}(a)$$ is the bilinear sampling kernel.

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