Image interpolation in the medical area is of vital importance as most 3D biomedical volume images are sampled where the distance between consecutive slices is significantly greater than the in-plane pixel size due to radiation dose or scanning time. Image interpolation creates a certain number of new slices between known slices in order to obtain an isotropic volume image. The results can be used for the higher quality of 2D and 3D visualization or reconstruction of human body structure. Semantic interpolation on the manifold has been proved to be very useful for smoothing the interpolation process. Nevertheless, all previous methods focused on low-resolution image interpolation, and most of which work poorly on high-resolution images. Besides, the medical field puts a high threshold for the quality of interpolations, as they need to be semantic and realistic enough, and resemble real data with only small errors permitted. Typically, people downsample the images into 322 and 642 for semantic interpolation, which does not meet the requirement for high-resolution in the medical field. Thus, we explore a novel way to generate semantically correct interpolations and maintain the resolution at the same time. Our method has been proved to generate realistic and high-resolution interpolations on the sizes of 5262 and 5122. Our main contribution is, first, we propose a novel network, High Resolution Interpolation Network (HRINet), aiming at producing semantically correct high-resolution CT image interpolations. Second, by combining the idea of ACAI and GANs, we propose a unique alternative supervision method by applying supervised and unsupervised training alternatively to raise the accuracy and fidelity of body structure in CT when interpolated while keeping high quality. Third, we introduce an extra Markovian discriminator as a texture or fine details regularizer to make our model generate results indistinguishable from real data. In addition, we explore other possibilities or tricks to further improve the performance of our model, including low-level feature maps mixing, and removing batch normalization layers within the autoencoder. Moreover, we compare the impacts of MSE based and perceptual based loss optimizing methods for high quality interpolation, and show the trade-off between the structural correctness and sharpness. The interpolation experiments show significant improvement on both sizes of 256 2 and 5122 images quantitatively and qualitatively. We find that interpolations produced by HRINet are sharper and more realistic compared with other existing methods such as AE and ACAI in terms of various metrics. As an application of high-resolution interpolation, we have done 2D volume projection and 3D volume reconstruction from axial view CT data and their interpolations. We show the great enhancement of applying HRINet for both in sharpness and fidelity. Specifically, for 2D volume projection, we explore orthogonal projection and weighted projection respectively so as to show the improved effectiveness for visualizing internal and external human body structure.