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A new proposed method of fully automatic processing frameworks is given based on Geodesic Graph-cut Active Contour algorithms. The algorithm is applied to image segmentation using two different kinds of local neighborhoods in constructing the graph. The major problem with Graph-Cut approach is the incorrect selection of Liver Region with coloring similar to user's scribbles being identified as a tumor region. Results can be improved by using the proposed new technique based on Geodesic Graph-Cut method. This system has concentrated on finding a fast and interactive segmentation method for liver and tumor segmentation. In the preprocessing stage, the CT image process is carried over with mean shift filter and statistical thresholding method for reducing processing area with improving detection rate. Second stage is Liver Segmentation; the liver region has been segmented using the algorithm of the proposed method. In the next stage, Tumor segmentation also followed the same steps. Finally the liver and tumor regions are separately segmented from the computer tomography image.