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Accurate image segmentation of the liver is a challenging problem owing to its large shape variability and unclear boundaries. Although the applications of fully convolutional neural networks (CNNs) have shown groundbreaking results, limited studies have focused on the performance of generalization. In this study, we introduce a CNN for liver segmentation on abdominal computed tomography (CT) images that shows high generalization performance and accuracy. To improve the generalization performance, we initially propose an auto-context algorithm in a single CNN. The proposed auto-context neural network exploits an effective high-level residual estimation to obtain the shape prior. Identical dual paths are effectively trained to represent mutual complementary features for an accurate posterior analysis of a liver. Further, we extend our network by employing a self-supervised contour scheme. We trained sparse contour features by penalizing the ground-truth contour to focus more contour attentions on the failures. The experimental results show that the proposed network results in better accuracy when compared to the state-of-the-art networks by reducing 10.31% of the Hausdorff distance. We used 180 abdominal CT images for training and validation. Two-fold cross-validation is presented for a comparison with the state-of-the-art neural networks. Novel multiple N-fold cross-validations are conducted to verify the performance of generalization. The proposed network showed the best generalization performance among the networks. Additionally, we present a series of ablation experiments that comprehensively support the importance of the underlying concepts.