Investigating multi-feature information-theoretic image registration, we introduce consistent and asymptotically unbiased kth-nearest neighbor (kNN) estimators of mutual information (MI), normalized MI and exclusive information applicable to high-dimensional random variables, and derive under closed-form their gradient flows over finite- and infinite-dimensional transform spaces. Using these results, we devise a novel unsupervised method for the groupwise registration of cardiac perfusion MRI exams. Here, local time-intensity curves are used as a dense set of spatio-temporal features, and statistically matched through variational optimization. Experiments on simulated and real datasets suggest the accuracy of the model for the affine registration of exams with up to 34 frames.