In this paper we propose a new method for the simultaneous segmentation and 3D reconstruction of interest point based articulated motion. We decompose a set of point tracks into rigid-bodied overlapping regions which are associated with skeletal links, while joint centres can be derived from the regions of overlap. This allows us to formulate the problem of 3D reconstruction as one of model assignment, where each model corresponds to the motion and shape parameters of an articulated body part. We show how this labelling can be optimised using a combination of pre-existing graph-cut based inference, and robust structure from motion factorization techniques. The strength of our approach comes from viewing both the decomposition into parts, and the 3D reconstruction as the optimisation of a single cost function, namely the image re-projection error. We show results of full 3D shape recovery on challenging real-world sequences with one or more articulated bodies, in the presence of outlie...