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The challenge of single-image dehazing mainly comes from double uncertainty of scene radiance and scene transmission. Most existing methods focus on restoring the visibility of hazy images and tend to derive a rough estimate of scene transmission. Unlike previous work, in this paper we advocate the significance of accurate transmission estimation and recast our problem as deriving the optimal transmission map directly from the haze model under two scene priors. We introduce theoretic and heuristic bounds of scene transmission to guide the optimum and show that the proposed theoretic bound happens to justify the well-known dark channel prior of haze-free images. With the constraints on the solution space, we then incorporate two scene priors, including locally consistent scene radiance and context-aware scene transmission, to formulate a constrained minimization problem and solve it by quadratic programming. The global optimality is guaranteed. Simulations on synthetic data set quantitatively verify the accuracy and show that the transmission map successfully captures fine-grained depth boundaries. Experimental results on color/gray-level images demonstrate that our method outperforms most state of the arts in terms of both accurate transmission maps and realistic haze-free images. [ABSTRACT FROM AUTHOR]