Differential and relaxed image foresting transform for graph-cut segmentation of multiple 3D objects.

Graph-cut algorithms have been extensively investigated for interactive binary segmentation, when the simultaneous delineation of multiple objects can save considerable user's time. We present an algorithm (named DRIFT) for 3D multiple object segmentation based on seed voxels and Differential Image Foresting Transforms (DIFTs) with relaxation. DRIFT stands behind efficient implementations of some state-of-the-art methods. The user can add/remove markers (seed voxels) along a sequence of executions of the DRIFT algorithm to improve segmentation. Its first execution takes linear time with the image's size, while the subsequent executions for corrections take sublinear time in practice. At each execution, DRIFT first runs the DIFT algorithm, then it applies diffusion filtering to smooth boundaries between objects (and background) and, finally, it corrects possible objects' disconnection occurrences with respect to their seeds. We evaluate DRIFT in 3D CT-images of the thorax for segmenting the arterial system, esophagus, left pleural cavity, right pleural cavity, trachea and bronchi, and the venous system.