Image segmentation by image foresting transform with geodesic band constraints

In this work, we propose a novel boundary constraint, which we denote as the Geodesic Band Constraint (GBC), and we show how it can be efficiently incorporated into a subclass of the Generalized Graph Cut framework (GGC). We include a proof of the optimality of the new algorithm in terms of a global minimum of an energy function subject to the new boundary constraints. The Geodesic Band Constraint helps regularizing the boundary, and consequently, improves the segmentation of objects with more regular shape, while keeping the low computational cost of the Image Foresting Transform (IFT). It can also be combined with the Geodesic Star Convexity prior, and with polarity constraints, at no additional cost. The method is demonstrated in CT thoracic studies of the liver, and MR images of the breast.