Nonrigid image registration methods based on the optimization of information-theoretic measures provide versatile solutions for robustly aligning mono-modal data with nonlinear variations and multi-modal data in radiology. Whereas mutual information and its variations arise as a first choice, generalized information measures offer relevant alternatives in specific clinical contexts. Their usual application setting is the alignement of image pairs by statistically matching scalar random variables (generally, greylevel distributions), handled via their probability densities. In this paper, we address the issue of estimating and optimizing generalized information measures over high-dimensional state spaces to derive multi-feature statistical nonrigid registration models. Specifically, we introduce novel consistent and asymptotically unbiaised k nearest neighbors estimators of α-informations, and study their variational optimization over finite and infinite dimensional smooth transform spaces. The resulting theoretical framework provides a well-posed and computationally efficient alternative to entropic graph techniques. Its performances are assessed on two cardiological applications: measuring myocardial deformations in tagged MRI, and compensating cardio-thoracic motions in perfusion MRI.