Graph　cut　based　interactive　image　segmentation　attracts　much　attention　in　recent　years.　Given　an　image,　traditional　methods　generally　need　users　to　indicate　parts　of　foreground　and　background　by　drawing　strokes,　etc.　Next,　these　methods　formulate　energy　functions,　which　are　generally　composed　of　color　and　gradient　constraints.　Considering　that　many　objects　to　be　cut　out　are　compact,　the　paper　presents　a　method　that　incorporates　a　simple　but　effective　direct　connectivity　constraint.　The　constraint　is　defined　geometrically　based　on　the　user　input　strokes.　The　centers　of　those　foreground　strokes　are　treated　as　foreground　representing　points.　Pixels　to　be　labeled,　which　are　not　directly　connected　to　the　representing　points,　i.e.　blocked　by　the　background　strokes　from　the　representing　points,　are　considered　to　belong　to　the　background.　Results　show　that　with　the　same　amount　of　user　interaction,　the　proposed　segmentation　method　obtains　better　results　than　state-of-the-art　ones.　©　2013　ACM.