assumptions: for every point on the image plane, there exists at least one input image that has reasonable exposure at that point: ∀(x_{0}, y_{0}) ∈ (x, y), ∃ k_{i}q(x_{0}, y_{0}) such that:

1. k_{i}q(x_{0}, y_{0}) >> n_{q_{i}}, and

2. c_{i} (q(x_{0}, y_{0})) >> c_{i} (\frac{1}{k_{i}} f^{−1}(n_{f_{i}}))