In the recent days, the segmentation of Liver Tumor (LT) has been demanding and challenging. The process of segmenting the liver and accurately spotting the tumor is demanding due to the diversity of shape, texture, and intensity of the liver image. The intensity similarities of the neighboring organs of the liver create difficulties during liver segmentation. The manual segmentation does not provide an accurate segmentation because the results provided by different medical experts can vary. Also, this manual technique requires a large number of image slices and time for segmentation. To solve these issues, the Fully Automatic Segmentation (FAS) technique is proposed. In this proposed Multi-Angle Texture Active Contour Model (MAT-ACM) method, the input Computed Tomography (CT) image is preprocessed by Contrast Enhancement (CE) with Non-Linear Mapping Technique (NLMT), in which the liver is differentiated from its neighbouring soft tissues with related strength. Then, the filtered images are given as the input to Adaptive Edge Modeling (AEM) with Canny Edge Detection (CED) technique, which segments the Liver Region (LR) from the given CT images. An AEM with a CED model is implemented, which increases the convergence speed of the iterative process for decreasing the Volumetric Overlap Error (VOE) is 6.92% rates when compared with the traditional Segmentation Techniques (ST). Finally, the Liver Tumor Segmentation (LTS) is developed by applying the MAT-ACM, which accurately segments the LR from the segmented LRs. The evaluation of the proposed method is compared with the existing LTS methods using various performance measures to prove the superiority of the proposed MAT-ACM method.