Perspective Nonrigid Shape and Motion Recovery

  • Authors:

  • Richard Hartley;René Vidal

  • Affiliations:

  • Australian National University and NICTA, Canberra, ACT, Australia;Center for Imaging Science, Johns Hopkins University, Baltimore, USA

  • Venue:
  • ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
  • Year:
  • 2008

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Abstract

We present a closed form solution to the nonrigid shape andmotion (NRSM) problem from point correspondences in multipleperspective uncalibrated views. Under the assumption that thenonrigid object deforms as a linear combination of Krigidshapes, we show that the NRSM problem can be viewed as areconstruction problem from multiple projections fromℙ3K to ℙ2. Therefore,one can linearly solve for the projection matrices by factorizing amultifocal tensor. However, this projective reconstruction inℙ3K does not satisfy the constraints ofthe NRSM problem, because it is computed only up to a projectivetransformation in ℙ3K . Our keycontribution is to show that, by exploiting algebraic dependenciesamong the entries of the projection matrices, one can upgrade theprojective reconstruction to determine the affine configuration ofthe points in ℝ3, and the motion of the camerarelative to their centroid. Moreover, if K≥ 2, theneither by using calibrated cameras, or by assuming a camera withfixed internal parameters, it is possible to compute the Euclideanstructure by a closed form method.