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Radiation therapy is one of the most effective options used in the treatment of about half of all people with cancer. A critical goal in radiation therapy is to deliver optimal radiation doses to the observed tumor while sparing the surrounding healthy tissues. Radiation oncologists typically manually delineate normal and diseased structures on three-dimensional computed tomography~(3D-CT) scans. Manual delineation is a labor intensive, tedious and time-consuming task. In recent years, concerns about respiration induced motion have led to the popularity of four-dimensional computed tomography~(4D-CT) for the tracking of tumors and deformation of organs. However, as manually contouring in all phases would be prohibitively expensive, the development of fast, robust, and automatic segmentation tools has been an active area of research in 4D radiotherapy. In this paper, we describe a novel application of principal surfaces for the propagation of contours in 4D-CT studies. Regions of interest~(ROIs) are manually delineated slice-by-slice in the reference 3D-CT scans. Edges are detected on all of the slices of the target 3D-CT phase. A kernel density estimation~(KDE) based on the detected edges is then calculated. The principal surface algorithm is applied to find the ridges of the edge KDE to provide the object contours. Manually drawn contours from the reference phase are used as an initialization. Contours of ROIs are propagated recursively in all consecutive phases to complete a respiration cycle. Results are provided for a phantom data set of simulated tumor motion as well as on a de-identified data set of the lung of a patient. Evaluation of the efficacy of automatic segmentation in organs and tumors are based on the comparison between manually drawn contours and automatically delineated contours. The Dice coefficients are approximately 0.97 for the lung tumor on the phantom data sets and 0.95 for the patient data sets. The centroid distances between manually deline- - ated lung volume and automatically segmented lung volume in each CT direction are <; 1 mm for both phantom data sets and patient data sets.