Anatomical structures and tissues are often hard to be segmented in medical images due to their poorly defined boundaries, i.e., low contrast in relation to other nearby false boundaries. The specification of the boundary polarity and the usage of shape constraints can help to alleviate part of this problem. Recently, an Oriented Image Foresting Transform (OIFT) has been proposed. In this work, we discuss how to incorporate Gulshan's geodesic star convexity prior in the OIFT approach for interactive image segmentation, in order to simultaneously handle boundary polarity and shape constraints. This convexity constraint eliminates undesirable intricate shapes, improving the segmentation of objects with more regular shape. We include a theoretical proof of the optimality of the new algorithm in terms of a global maximum of an oriented energy function subject to the shape constraints, and show the obtained gains in accuracy using medical images of thoracic CT studies. © 2013 Springer-Verlag.