Transmission map estimation is one of the most important parts of single image dehazing, which is known as an under-constraint problem. Various assumptions, some have been summarized as priors or models, are proposed to solve this problem. However, many previous methods cannot honestly reflect their theory in the results, due to not considering all of the employed assumptions simultaneously. Meanwhile, most other methods avoiding this defect are with inappropriate assumptions. We try to solve this problem by proposing a method that simultaneously considers the dark channel prior and the piecewise smoothness assumption. It is achieved by minimizing an energy function based on all of the employed assumptions. To maintain a reasonable run time, the minimization problem is mapped into a graph cut problem with a specific graph build strategy. The method is compared with state-of-the-art methods on both synthetic and natural images. Experimental results show that the proposal is promising for haze removal quality.