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The paper presents the automated computation of hepatic tumor burden from abdominal computed tomography (CT) images of diseased populations with images with inconsistent enhancement. The automated segmentation of livers is addressed first. A novel 3-D affine invariant shape parameterization is employed to compare local shape across organs. By generating a regular sampling of the organ's surface, this parameterization can be effectively used to compare features of a set of closed 3-D surfaces point-to-point, while avoiding common problems with the parameterization of concave surfaces. From an initial segmentation of the livers, the areas of atypical local shape are determined using training sets. A geodesic active contour corrects locally the segmentations of the livers in abnormal images. Graph cuts segment the hepatic tumors using shape and enhancement constraints. Liver segmentation errors are reduced significantly and all tumors are detected. Finally, support vector machines and feature selection are employed to reduce the number of false tumor detections. The tumor detection true position fraction of 100% is achieved at 2.3 false positives/case and the tumor burden is estimated with 0.9% error. Results from the test data demonstrate the method's robustness to analyze livers from difficult clinical cases to allow the temporal monitoring of patients with hepatic cancer.