Simultaneous camera pose, 4D reconstruction of an object and deformation clustering from incomplete 2D point tracks in a video is a challenging problem. To solve it, in this work we introduce a union of piecewise subspaces to encode the 4D shape, where two modalities based on B-splines and Catmull-Rom curves are considered. We demonstrate that formulating the problem in terms of B-spline or Catmull-Rom functions, allows for a better physical interpretation of the resulting priors while C1 and C2 continuities are automatically imposed without needing any additional constraint. An optimization framework is proposed to sort out the problem in a unified, accurate, unsupervised and efficient manner. We extensively validate our claims on a wide range of human motions, including articulated and continuous deformations as well as those cases with noisy and missing measurements where our approach provides competing joint solutions.

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