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In this paper we introduce a new shape constraint for interactive image segmentation. It is an extension of Veksler's star-convexity prior, in two ways: from a single star to multiple stars and from Euclidean rays to Geodesic paths. Global minima of the energy function are obtained subject to these new constraints. We also introduce Geodesic Forests, which exploit the structure of shortest paths in implementing the extended constraints. The star-convexity prior is used here in an interactive setting and this is demonstrated in a practical system. The system is evaluated by means of a “robot user” to measure the amount of interaction required in a precise way. We also introduce a new and harder dataset which augments the existing Grabcut dataset with images and ground truth taken from the PASCAL VOC segmentation challenge.