Algorithm 1. Spatial-Motion Segmentation

Start

Input: Raw events, set ${\epsilon }_1={\left\{e_k=\left(x_k,y_k,t_k,p_k\right)\right\}}_{k=1}^{N_e}$; original images; the number of clusters ($N_l$).

Output: Event-cluster membership probabilities ($\mathbf{P}$), and motion parameters ($\mathit{\theta }$).

Procedure:

1:For each image, do depth estimation.

End for;

2: For$k\leftarrow 1$ to $N_e$, do:

$Z_k=\frac{t_k-T_{fram{e}_1}}{T_{fram{e}_2}-T_{fram{e}_1}}\left|Z_{fram{e}_2}-Z_{fram{e}_1}\right|$

$Z_k\left[\begin{array}{c}{x}_k\\ y_k\\ 1\end{array}\right]=\left[\begin{array}{ccc}f& 0& 0\\ 0& f& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{X}_k\\ Y_k\\ Z_k\end{array}\right]$

End for:

${\epsilon }_2={\left\{e_k=\left(X_k,Y_k,Z_k,t_k,p_k\right)\right\}}_{k=1}^{N_e}$

3:For$e_k$, do:

computing ${\mathit{\theta }}_k$ according to $\mathit{\theta }={\left({\theta }_x,\frac{-a_1{\theta }_x+c_1}{b_1},\frac{-b_3{\theta }_x+c_3}{a_3}\right)}^T$

End for:

4: For$k\leftarrow 1$ to $N_e$, do:

warping $e_k$ according to ${\mathbf{x}}_k^{\prime }={\mathbf{x}}_k-\left(t_k-t_{ref}\right)\mathit{\theta }={\mathbf{x}}_k-\Delta t_k\mathit{\theta }$

End for:

5: For each warped $e_k$, do weighted accumulate:

$V_j\left(\mathbf{x}\right)={\displaystyle \sum _{k=1}^{N_e}{p}_{kj}}\delta \left(\mathbf{x}-{\mathbf{x}}_{kj}^{\prime }\right)$

6: For$i\leftarrow 1$ to $\infty$, do:

If the variance is not converged, then:

update the $\mathbf{P}$ using $p_{kj}=\frac{c_j({\mathbf{x}}_k^{\prime }({\mathit{\theta }}_j))}{{\displaystyle \sum _{i=1}^{N_l}{c}_i({\mathbf{x}}_k^{\prime }({\mathit{\theta }}_i))}}$

update the $\mathit{\theta }$ according to SSA-Gradient Ascent:

computing $Var\left(V_j\right)={{\displaystyle \sum _{a,b,c\in \mathrm{\Omega }}\left(V_{abc}-{\mu }_{V_j}\right)}}^2$

End if:

$i\leftarrow i+1$

End for:

End