In many biological or medical applications, images that contain sequences of shapes are common. The existence of high inter-individual variability makes their interpretation complex. In this paper, we address the computer-assisted interpretation of such images and we investigate how we can remove or reduce these image variabilities. The proposed approach relies on the development of an efficient image registration technique. We first show the inadequacy of state-of-the-art intensity-based and feature-based registration techniques for the considered image datasets. Then, we propose a robust variational method which benefits from the geometrical information present in this type of images. In the proposed non-rigid geodesics-based registration, the successive shapes are represented by a level-set representation, which we rely on to carry out the registration. The successive level sets are regarded as elements in a shape space and the corresponding matching is that of the optimal geodesic path. The proposed registration scheme is tested on synthetic and real images. The comparison against results of state-of-the-art methods proves the relevance of the proposed method for this type of images.