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Geodesic Shooting and Diffeomorphic Matching Via Textured Meshes

  • Stéphanie Allassonnière
  • Alain Trouvé
  • Laurent Younes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3757)

Abstract

We propose a new approach in the context of diffeomorphic image matching with free boundaries. A region of interest is triangulated over a template, which is considered as a grey level textured mesh. A diffeomorphic transformation is then approximated by the piecewise affine deformation driven by the displacements of the vertices of the triangles. This provides a finite dimensional, landmark-type, reduction for this dense image comparison problem. Based on an optimal control model, we analyze and compare two optimization methods formulated in terms of the initial momentum: direct optimization by gradient descent, or root-finding for the transversality equation, enhanced by a preconditioning of the Jacobian. We finally provide a series of numerical experiments on digit and face matching.

Keywords

Transversality Condition Image Match Initial Momentum Gradient Descent Algorithm Handwritten Digit 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Stéphanie Allassonnière
    • 1
  • Alain Trouvé
    • 2
  • Laurent Younes
    • 3
  1. 1.LAGA, Institut GaliléeUniversity Paris 13France
  2. 2.CMLAEcole Normale SupérieureCachanFrance
  3. 3.CISJohns Hopkins UniversityBaltimore

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