In this work we introduce a new dissimilarity measure for shape registration using the notion of normal cycles, a concept from geometric measure theory which allows to generalize curvature for non smooth subsets of the euclidean space. Our construction is based on the definition of kernel metrics on the space of normal cycles which take explicit expressions in a discrete setting. This approach is closely similar to previous works based on currents and varifolds [13,5]. We derive the computational setting for discrete curves in R 3 , using the Large Deformation Diffeomorphic Metric Mapping framework as model for deformations. We present synthetic experiments and compare with the currents and varifolds approaches.