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.　(c)　2017　Society　of　Photo-Optical　Instrumentation　Engineers　(SPIE)