Tensor Voting : Theory and Applications

  • Medioni G
  • Lee M
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Abstract

We present a unified computational framework which properly implements
the smoothness constraint to generate descriptions in terms of surfaces,
regions, curves, and labelled junctions, from sparse, noisy, binary
data in 2-D or 3-D. Each input site can be a point, a point with
an associated tangent direction, a point with an associated normal
direction, or any combination of the above. The methodology is grounded
on two elements: tensor calculus for representation, and linear voting
for communication: each input site communicates its information (a
tensor) to its neighborhood through a predefined (tensor) field,
and therefore casts a (tensor) vote. Each site collects all the votes
cast at its location and encodes them into a new tensor. A local,
parallel marching process then simultaneously detects features. The
proposed approach is very different from traditional variational
approaches, as it is non-iterative. Furthermore, the only free parameter
is the size of the neighborhood, related to the scale. We have developed
several algorithms based on the proposed methodology to address a
number of early vision problems, including perceptual grouping in
2-D and 3-D, shape from stereo, and motion grouping and segmentation,
and the results are very encouraging.

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Authors

  • Gérard Medioni

  • Mi-Suen Lee

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