In this paper, we propose a Markov random field-based method that uses saliency and gradient information for elastic registration of dynamic contrast enhanced (DCE) magnetic resonance (MR) images of the heart. DCE-MR images are characterized by rapid intensity changes over time, thus posing challenges for conventional intensity-based registration methods. Saliency information contributes to a contrast invariant metric to identify similar regions in spite of contrast enhancement. Its robustness and accuracy are attributed to a close adherence to a neurobiological model of the human visual system (HVS). The HVS has a remarkable ability to match images in the face of intensity changes and noise. This ability motivated us to explore the efficacy of such a model for registering DCE-MR images. The data penalty is a combination of saliency and gradient information. The smoothness cost depends upon the relative displacement and saliency difference of neighboring pixels. Saliency is also used in a modified narrow band graph cut framework to identify relevant pixels for registration, thus reducing the number of graph nodes and computation time. Experimental results on real patient images demonstrate superior registration accuracy for a combination of saliency and gradient information over other similarity metrics.