deletions | additions       diff --git a/section_MRF_based_Energy_Minimization__.tex b/section_MRF_based_Energy_Minimization__.tex  index 1bba0d0..f28dd87 100644  --- a/section_MRF_based_Energy_Minimization__.tex  +++ b/section_MRF_based_Energy_Minimization__.tex 
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\begin{equation}  E(X) = \sum_{i \sum_{u_i  \in X} E_{1} E_{1}(u_i)  + \lambda \sum_{(i,j) \sum_{(u_i,u_j)  \in X} E_{2}(i,j) E_{2}(u_i,u_j)  \end{equation} 
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\textbf{Likelihood}, $E_1$, is defined as:  \begin{equation}  E_1(x_r) E_1(u_i)  = \sum_{x_j \in r} w^{c_j} 1 - exp(\frac{1}{\sigma_{data}^2}(Pr(l_i|u_i)))  \end{equation}  \textbf{Prior energy}, $E_2$, simply measures the label agreement between adjacent nodes, defined as: