Precise segmentation of the liver is critical for computer-aided diagnosis such as pre-evaluation of the liver for living donor-based transplantation surgery. This task is challenging due to the weak boundaries of organs, countless anatomical variations, and the complexity of the background. Computed tomography (CT) scanning and magnetic resonance imaging (MRI) images have different parameters and settings. Thus, images acquired from different modalities differ from one another making liver segmentation challenging task. We propose an efficient liver segmentation with the combination of holistically-nested edge detection (HED) and Mask- region-convolutional neural network (R-CNN) to address these challenges. The proposed HED-Mask R-CNN approach is based on effective identification of edge map from multimodal images. The proposed system firstly applies a preprocessing step of image enhancement to get the ‘primal sketches’ of the abdomen. Then the HED network is applied to enhanced CT and MRI modality images to get better edge map. Finally, the Mask R-CNN is used to segment the liver from edge map images. We used a dataset of 20 CT patients and 9 MR patient from the CHAOS challenge. The system is trained on CT and MRI images separately and then converted to 2D slices. We significantly improved the segmentation accuracy of CT and MRI images on a database with Dice value of 0.94 for CT, 0.89 for T2-weighted MRI and 0.91 for T1-weighted MRI.