Hepatocellular carcinoma leads to more human deaths currently. Patient survival rates can be increased by early detection of the tumor which is the main problem. In many cases, the task of early detection in liver grayscale images is very complicated since the intensity values between healthy and abnormal tissues may be very similar. In this paper, a pre-processing step of pixel colors is introduced to determine the pathology that is being observed, then, followed by a robust detection technique for liver PET/CT images using a k-means clustering algorithm based on pixel intensity optimization and evaluation of probability distribution functions. In this method, k cluster centers are changed with the distance between each pixel to each cluster center. This includes three main stages: pre-processing, segmentation, and measuring the percentage of the region having carcinoma. The unwanted regions can be removed from the segmented image by using the median filter. This work consisted of a comparative study of certain segments of medical image techniques in order to determine as accurately as possible when estimating quality segmentation from performance measures, such as Peak Signal-to-Noise Ratio, percentage of tumor detection, segmentation error, and coefficient similarity dice. The algorithm is applied to 60 sets of different real data in the form of liver PET/CT images with and without tumor tissues. The simulation results showed better detection was obtained using the proposed method.