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\noindent assumptions: for every point on the image\\
plane, there exists at least one input image\\
that has reasonable exposure at that point:
%overcome sensor noise, and that
%this exposure is not lost in the toe or shoulder of the
%response curve:
\\
$\forall (x_0,y_0) \in (x,y), \;\; \exists \; k_i q(x_0,y_0)$
such that:
\begin{enumerate}
  \item $k_i q(x_0,y_0) >> n_{q_i}$, and
  \item $c_i\left(q(x_0,y_0)\right)
   >> c_i\left(\frac{1}{k_i}f^{-1}(n_{f_i})\right)$
\end{enumerate}
\end{document}

