Geodesic interpolating splines

Abstract

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