Geodesic Interpolating Splines

We propose a simple and eecient method to interpolate landmark matching by a non-ambiguous mapping (a diieomorphism). This method is based on spline interpolation, and on recent techniques developed for the estimation of ows of diieomorphisms. Experimental results show interpolations of remarkable quality. Moreover, the method provides a Riemannian distance on sets of landmarks (with xed car-dinality), which can be deened intrinsically, without refering to diieo-morphisms. The numerical implementation is simple and eecient, based on an energy minimization by gradient descent. This opens important perspectives for shape analysis, applications in medical imaging, or computer graphics