while Not Converged do

for i in $\{1,2\}$ do ▹Inverse warping

$c_{i2}\leftarrow c_{i1}◦{\phi }^{-1}$

for $i,j$ in $\{1,2\}$ do ▹Forward-projection

$c_{\mathit{ij}}^F(y)\leftarrow {\sum }_{x}h(x,y)c_{\mathit{ij}}(x)$

for j in {1, 2} do ▹Basis vector model

$q_j(y,E)\leftarrow I_{0,j}(y,E)e^{-{\sum }_i{\mu }_i(E)c_{\mathit{ij}}^F(y)}$

for $i,j$ in $\{1,2\}$ do

${\tilde{g}}_{\mathit{ij}}(y)\leftarrow {\sum }_E{\mu }_i(E)q_j(y,E)$

${\tilde{d}}_{\mathit{ij}}(y)\leftarrow \frac{{\sum }_E{\mu }_i(E)q_j(y,E)d_j(y)}{{\sum }_{E\prime }{q}_j(y,E\prime )}$

for $i,j$ in $\{1,2\}$ do ▹Back-projection

$g_{\mathit{ij}}^B(x)\leftarrow {\sum }_{y}h(x,y){\tilde{g}}_{\mathit{ij}}(y)$

$d_{\mathit{ij}}^B(x)\leftarrow {\sum }_{y}h(x,y){\tilde{d}}_{\mathit{ij}}(y)$

for i in $\{1,2\}$ do ▹Forward warping

$g_{i2}^B(x)\leftarrow g_{i2}^B(x)◦\phi$

$d_{i2}^B(x)\leftarrow d_{i2}^B(x)◦\phi$

Solve decoupled function ▹Image update

${\mathrm{argmin}}_{c_{i1}}{\sum }_j{\sum }_i{\sum }_x\left[d_{\mathit{ij}}^B(x)c_{i1}^{\mathit{new}}+g_{\mathit{ij}}^B(x)\frac{1}{Z_i(x)}·\right.$

$\left.\exp (Z_i(x)[c_{i1}^{\mathit{old}}(x)-c_{i1}^{\mathit{new}}(x)])\right]+R({\mathbf{c}}^{k+1})$

outputs:

$c_1=c_{11}$, $c_2=c_{21}$