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\f$ E(\bar{x}) = \sum\limits_{f \in F} e_1(f, x_f) + \lambda \sum\limits_{ \{f,g\} \in N} e_2(x_f, x_g) \f$
\f$ e_1(f, x_f) = -log(max(P(f|x_f), \epsilon)) \f$
- \f$ e_2(x_f, x_g) =
- \left \{
+ \f$ e_2(x_f, x_g) =
+ \left \{
\begin{array}{rl}
-log(\theta(f,g)/\pi) &\mbox{ $x_f \ne x_g$} \\
0 &\mbox{ $x_f = x_g$}
\end{array}
\right \} \f$
- |
-
+ |
+
where:
- - \f$F\f$ is the set of facets,
+ - \f$F\f$ is the set of facets,
- \f$N\f$ is the set of pairs of neighbor facets,
- - \f$x_f\f$ is the cluster assigned to facet \f$f\f$,
- - \f$P(f|x_p)\f$ is the probability of assigning facet \f$f\f$ to cluster \f$x_p\f$,
- - \f$\theta(f,g)\f$ is the dihedral angle between neighbor facets \f$f\f$, and \f$g\f$,
+ - \f$x_f\f$ is the cluster assigned to facet \f$f\f$,
+ - \f$P(f|x_p)\f$ is the probability of assigning facet \f$f\f$ to cluster \f$x_p\f$,
+ - \f$\theta(f,g)\f$ is the dihedral angle between neighbor facets \f$f\f$, and \f$g\f$,
concave angles and convex angles are weighted by 1 and 0.1 respectively,
- \f$\epsilon\f$ is the minimal probability threshold,
- \f$\lambda \in [0,1]\f$ is a smoothness parameter.
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-
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