In this paper we present a new approach for non rigid groupwise registration of cardiac magnetic resonance images by means of free-form deformations, imposing a prior harmonic deformation assumption. The procedure proposes a primal-dual framework for solving an equality constrained minimization problem, which allows an automatic estimate of the trade-off between image fi- delity and the Laplacian smoothness terms for each iteration. The method has been applied to both a 4D extended cardio-torso phantom and to a set of voluntary patients. The accuracy of the method has been measured for the synthetic experiment as the dif- ference in modulus between the estimated displacement field and the ground truth; as for the real data, we have calculated the Dice coefficient between the contour manual delineations provided by two cardiologists at end systolic phase and those provided by them at end diastolic phase and, consequently propagated by the registration algorithm to the systolic instant. The automatic pro- cedure turns out to be competitive in motion compensation with other methods even though their parameters have been previously set for optimal performance in different scenarios.
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