Precise liver segmentation in Computed Tomography (CT) scans plays a pivotal role in numerous biomedical applications, spanning surgical planning, postoperative assessment, and pathological detection of hepatic diseases. The task, however, is fraught with challenges due to the inherent complexities of liver morphology, including indistinct boundaries, irregular shapes, and complex architecture. Consequences of under-segmentation and oversegmentation of the liver in CT images can lead to inaccurate localizations and diagnoses of liver diseases, underscoring the necessity for accurate segmentation. This study introduces an Encoder-Decoder Convolutional Neural Network, termed ESP-UNet, which is designed to reduce under-segmentation and over-segmentation, thereby enhancing the accuracy of liver segmentation. The proposed ESP-UNet employs Kirsch's filter to bolster the texture and edge information of liver images, thus aiding in improved segmentation performance. The efficacy of the ESP-UNet segmentation technique was evaluated using the LiTS dataset, with performance metrics including accuracy, Dice Score Coefficient (DSC), Volume Overlapping Error (VOE), and Relative Volume Difference (RVD). The algorithm yielded impressive results, with a Dice Score of 0.959, a VOE of 0.089, a Jaccard Index (JI) of 0.921, and an RVD of 0.09. Despite requiring a larger number of trainable parameters and an increased network complexity due to the parallel UNet, the proposed ESP-UNet not only enhances liver segmentation but also has the potential to improve the detection of liver cancer at the image borders. A comparison with existing state-of-the-art liver segmentation techniques revealed that ESP-UNet offers superior performance, validating its potential as a useful tool in the diagnosis and treatment of liver diseases.