The segmentation of liver margins in computed tomography (CT) images presents significant challenges due to the complex anatomical variability of the liver, with critical implications for medical diagnostics and treatment planning. In this study, we leverage a substantial dataset of over 4,200 abdominal CT images, meticulously annotated by expert radiologists from Taleghani Hospital in Kermanshah, Iran. Now made available to the research community, this dataset serves as a rich resource for enhancing and validating various neural network models. We employed two advanced deep neural network models, U-Net and Detectron2, for liver segmentation tasks. In terms of the Mask Intersection over Union (Mask IoU) metric, U-Net achieved an Mask IoU of 0.903, demonstrating high efficacy in simpler cases. In contrast, Detectron2 outperformed U-Net with an Mask IoU of 0.974, particularly excelling in accurately delineating liver boundaries in complex cases where the liver appears segmented into two distinct regions within the images. This highlights Detectron2's advanced potential in handling anatomical variations that pose challenges for other models. Our findings not only provide a robust comparative analysis of these models but also establish a framework for further enhancements in medical imaging segmentation tasks. The initiative aims not just to refine liver margin detection but also to facilitate the development of automated systems for diagnosing liver diseases, with potential future applications extending these methodologies to other abdominal organs, potentially transforming the landscape of computational diagnostics in healthcare.