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In computed tomography of liver tumors there is often heterogeneous density, weak boundaries, and the liver tumors are surrounded by other abdominal structures with similar densities. These pose limitations to accurate the hepatic tumor segmentation. We propose a level set model incorporating likelihood energy with the edge energy. The minimization of the likelihood energy approximates the density distribution of the target and the multimodal density distribution of the background that can have multiple regions. In the edge energy formulation, our edge detector preserves the ramp associated with the edges for weak boundaries. We compared our approach to the Chan-Vese and the geodesic level set models and the manual segmentation performed by clinical experts. The Chan-Vese model was not successful in segmenting hepatic tumors and our model outperformed the geodesic level set model. Our results on 18 clinical datasets showed that our algorithm had a Jaccard distance error of 14.4 ± 5.3%, relative volume difference of -8.1 ± 2.1%, average surface distance of 2.4 ± 0.8 mm, RMS surface distance of 2.9 ± 0.7 mm, and the maximum surface distance of 7.2 ± 3.1 mm.