This paper presents a novel methodology for the non-rigid registration of cardiac perfusion MRI exams. The target medical application is the automated quantitative assessment of myocardial perfusion for clinical diagnosis and longitudinal study of ischemic pathologies. Specifically, an original variational method for the groupwise registration of p-MRI exams based on high-dimensional feature distribution matching using (normalized) mutual information, is developed. The hard issue of estimating information in high-dimensional spaces is solved using state-of-the-art kth-nearest neighbor (kNN) entropy estimators. Combined with mean-shift approximation, the latter allow to efficiently optimize (normalized) mutual information over finite- and infinite-dimensional motion spaces. This framework is applied to the groupwise alignment of cardiac p-MRI exams using local contrast enhancement curves as a feature set, and a B-spline model for cardio-thoracic motions. Preliminary experimental assessment suggests that the technique allows for accurately aligning up to 34 p-MRI images simultaneously, and for further reliably computing perfusion parameters whose joint analysis strongly correlates with expert-based visual diagnosis.