This article substantially advances upon state-of-the-art to enhance liver vessels segmentation accuracy by leveraging advantages of synthetic PET-CT (SPET-CT) images in addition to computed tomography angiography (CTA) volumes. Our setup makes a hybrid solution of modified generative adversarial network-convolutional autoencoder (GAN-cAED) combining synthetic ability of GAN to deliver SPET-CT images with generative ability of cAED network in terms of latent learning to more refined segmentation of major liver vessels. We improve time complexity through a novel concept of controlled segmentation by introducing a threshold metric to stop segmentation up to a desired level. The innovative concept of controlled vessel segmentation with a stopping criterion via variant threshold levels will help surgeons to avoid unintentional major blood vessels cutting, reducing the risk of excessive blood loss. Clinically, such solutions offer computer-aided liver surgeries and drug treatment evaluation in a CTA-only environment, shorten the requirement of radioactive and expensive fused PET-CT images.