Interactive volume segmentation with differential image foresting transforms

The absence of object information very often asks for considerable human assistance in medical image segmentation. Many interactive two-dimensional and three-dimensional (3-D) segmentation methods have been proposed, but their response time to user's actions should be considerably reduced to make them viable from the practical point of view. We circumvent this problem in the framework of the image foresting transform (IFT)-a general tool for the design of image operators based on connectivity-by introducing a new algorithm (DIFT) to compute sequences of IFTs in a differential way. We instantiate the DIFT algorithm for watershed-based and fuzzy-connected segmentations under two paradigms (single-object and multiple-object) and evaluate the efficiency gains of both approaches with respect to their linear-time implementation based on the nondifferential IFT. We show that the DIFT algorithm provides efficiency gains from 10 to 17, reducing the user's waiting time for segmentation with 3-D visualization on a common PC from 19-36 s to 2-3 s. We also show that the multiple-object approach is more efficient than the single-object paradigm for both segmentation methods.