The accurate measurement of 3D cardiac function is an important task in the analysis of cardiac magnetic resonance (MR) images. However, short-axis image acquisitions with thick slices are commonly used in clinical practice due to constraints of acquisition time, signal-to-noise ratio and patient compliance. In this situation, the estimation of a high-resolution image can provide an approximation of the underlaying 3D measurements. In this paper, we develop a novel algorithm for the estimation of high-resolution cardiac MR images from single short-axis cardiac MR image stacks. First, we propose to use a novel approximate global search approach to find patch correspondence between the short-axis MR image and a set of atlases. Then, we propose an innovative super-resolution model which does not require explicit motion estimation. Finally, we build an expectation-maximization framework to optimize the model. We validate the proposed approach using images from 19 subjects with 200 atlases and show that the proposed algorithm significantly outperforms conventional interpolation such as linear or B-spline interpolation. In addition, we show that the super-resolved images can be used for the reproducible estimation of 3D cardiac functional indices.