In this paper we address the problem of jointly retrieving a 3D dynamic shape, camera motion, and deformation grouping from partial 2D point trajectories in a monocular video. To this end, we introduce a union of piecewise Bézier subspaces with enforcing continuities to model 3D motion. We show that formulating the problem in terms of piecewise curves, allows for a better physical interpretation of the resulting priors and a more accurate representation of the motion. An energy-based formulation is presented to solve the problem in an unsupervised, unified, accurate and efficient manner, by means of the use of augmented Lagrange multipliers. We thoroughly validate the approach on a wide variety of human video sequences, including those cases with noisy and missing observations, and providing more accurate joint estimations than state-of-the-art approaches.