1. Introduction
Non-Rigid Shape-from-Motion (NRSfM) is the problem of finding the 3D shape of a deforming object given a set of monocular images. This problem is naturally under-constrained because there can be many different deformations that produce the same images. By including deformation constraints one limits the set of solutions. Several methods have been proposed in the last decade to tackle NRSfM with a variety of deformation constraints. There are two main categories of methods based on the deformation constraints: statistics-based [27], [14], [5], [10], [12] and physics-based [26], [30], [7], [29], [2] methods. In the former group one assumes that the space of deformations is low-dimensional. These methods are accurate for deformations such as body gestures, facial expressions and simple smooth deformations. However they tend to perform poorly for objects with high-dimensional deformation spaces or atypical deformations. They can also be difficult to use when there is missing data due to e.g. occlusions. In the latter group one finds deformation models based on isometry [7], [26], [30], [29], elasticity [1] or particle-interaction models [2]. The isometric model is especially interesting and is an accurate model for a great variety of real objects. In the related problem of template-based reconstruction (also referred to as Shape-from-Template [4]) it has been proven to make the problem well-posed [23], [18], [4], [8]. However in NRSfM, approaches based on isometry still lack in several aspects. For example solutions tend to be complex and often require very good initialization.