How can we represent shape?

• Point-wise representation and Shape Spaces

  Feature points must be visible from frame to frame (correspondence problem)
  - Feature points appear and disappear due to occlusions
  - Sparse representation of the world (not good for visualization)
  + No model is imposed on the data (all geometric constraints are exact).

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• Models for shape

  Constraints are imposed on the shape of the environment, for instance
  • points have support on a parametric Surface Model
  • the environment consists of simple geometric objects (cubes, spheres, cones) [Malik et al.]
  • the environment has a special structure
    such as a freeway [Dickmanns et al.], the interior of a building, a human face etc.
  - Choice of the model class and the order of parametric models is non-trivial
  - issues related to local/global modeling + dense representation of the world: low-level
  features (such as points, lines or curves in 3-D) are grouped together.