Statistical cue integration in DAG deformable models

Siome Klein Goldenstein, Christian Vogler, Dimitris Metaxas

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


Deformable models are a useful modeling paradigm in computer vision. A deformable model is a curve, a surface, or a volume, whose shape, position, and orientation are controlled through a set of parameters. They can represent manufactured objects, human faces and skeletons, and even bodies of fluid. With low-level computer vision and image processing techniques, such as optical flow, we extract relevant information from images. Then, we use this information to change the parameters of the model iteratively until we find a good approximation of the object in the images. When we have multiple computer vision algorithms providing distinct sources of information (cues), we have to deal with the difficult problem of combining these, sometimes conflicting contributions in a sensible way. In this paper, we introduce the use of a directed acyclic graph (DAG) to describe the position and Jacobian of each point of deformable models. This representation is dynamic, flexible, and allows computational optimizations that would be difficult to do otherwise. We then describe a new method for statistical cue integration method for tracking deformable models that scales well with the dimension of the parameter space. We use affine forms and affine arithmetic to represent and propagate the cues and their regions of confidence. We show that we can apply the Lindeberg theorem to approximate each cue with a Gaussian distribution, and can use a maximum-likelihood estimator to integrate them. Finally, we demonstrate the technique at work in a 3D deformable face tracking system on monocular image sequences with thousands of frames.

Original languageEnglish (US)
Pages (from-to)801-813
Number of pages13
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number7
StatePublished - Jul 2003

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


  • Affine arithmetic
  • Deformable model representation
  • Deformable model tracking
  • Directed acyclic graphs
  • Face tracking
  • Statistical cue integration


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