Compensating for cardio-thoracic motion artifacts in contrast-enhanced cardiac perfusion MRI (p-MRI) sequences is a key issue for the quantitative assessment of myocardial ischæmia. The classical paradigm consists of registering each sequence frame on some reference using an intensity-based matching criterion. In this paper, we present a novel unsupervised method for the groupwise registration of cardiac p-MRI exams based on mutual information between high-dimensional feature distributions. Specifically, local contrast enhancement curves are used as a dense set of spatio-temporal features, and statistically matched to a target feature distribution derived from a registered reference template. Using consistent kth nearest neighbors entropy estimators further enables the variational optimization of the model over finite- and infinite dimensional transform spaces. Experiments on simulated and natural datasets demonstrate its accuracy and relevance for the reliable assessment of regional perfusion.