Authorea

Model

We denote the input image by \(I\), output by \(Y\), set of parameters by \(\Theta\).

Conditional Random Fields(CRF).

\begin{equation} S(I,Y,\Theta)=\sum_{i\in V}{\Phi_{i}(I,Y_{i},\Theta)+\sum_{ij\in E}{\Psi_{ij}(I,Y_{i},Y_{j},\Theta)}}\\ \end{equation}

\begin{equation} \Psi_{ij}(I,Y_{i},Y_{j},\Theta)=\sum_{m=1}^{M}{w_{m}k_{m}(f(Y_{i}),f(Y_{j}))}\\ \end{equation}

\begin{equation} Y^{*}=\operatorname*{arg\,max}_{Y}{S(I,Y,\Theta)}\\ \end{equation}