Simultaneous detection of multiple elastic surfaces with application to tumor segmentation in CT images

We present a new semi-supervised method for segmenting multiple interrelated object boundaries with spherical topology in volumetric images. The core of our method is a novel graph-theoretic algorithm that simultaneously detects multiple surfaces under smoothness, distance, and elasticity constraints. The algorithm computes the global optimum of an objective function that incorporates boundary, regional and surface elasticity information. A single straight line drawn by the user in a cross-sectional slice is the sole user input, which roughly indicates the extent of the object. We employ a multi-seeded Dijkstra-based range competition algorithm to pre-segment the object on two orthogonal multiplanar reformatted (MPR) planes that pass through the input line. Based on the 2D pre-segmentation results, we estimate the object and background intensity histograms, and employ an adaptive mean-shift mode-seeking process on the object histogram to automatically determine the number of surface layers to be segmented. The final multiple-surface segmentation is performed in an ellipsoidal coordinate frame constructed by an automated ellipsoid fitting procedure. We apply our method to the segmentation of liver lesions with necrosis or calcification, and various other tumors in CT images. For liver tumor segmentation, our method can simultaneously delineate both tumor and necrosis boundaries. This capability is unprecedented and is valuable for cancer diagnosis, treatment planning, and evaluation.