Automatic estimation of axial spine indices is clinically desired for various spine computer aided procedures, such as disease diagnosis, therapeutic evaluation, pathophysiological understanding, risk assessment, and biomechanical modeling. Currently, the spine indices are manually measured by physicians, which is time-consuming and laborious. Even worse, the tedious manual procedure might result in inaccurate measurement. To deal with this problem, in this paper, we aim at developing an automatic method to estimate multiple indices from axial spine images. Inspired by the success of deep learning for regression problems and the densely connected network for image classification, we propose a dense enhancing network (DE-Net) which uses the dense enhancing blocks (DEBs) as its main body, where a feature enhancing layer is added to each of the bypass in a dense block. The DEB is designed to enhance discriminative feature embedding from the intervertebral disc and the dural sac areas. In addition, the cross-space distance-preserving regularization (CSDPR), which enforces consistent inter-sample distances between the output and the label spaces, is proposed to regularize the loss function of the DE-Net. To train and validate the proposed method, we collected 895 axial spine MRI images from 143 subjects and manually measured the indices as the ground truth. The results show that all deep learning models obtain very small prediction errors, and the proposed DE-Net with CSDPR acquires the smallest error among all methods, indicating that our method has great potential for spine computer aided procedures.