Abstract: 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.