3D Curves Reconstruction Based on Deformable Models

  • Authors:

  • Catalina Sbert;Andreas F. Solé

  • Affiliations:

  • Departament de Matemàtiques i Informàtica, Universitat de les Illes Balears Crta de Valldemossa, Km 7.5, 07071 Palma de Mallorca, Spain. dmicsj0@clust.uib.es;Universitat Pompeu Fabra, Pg. de Circumval.lacio, I, Barcelona, Spain. andreu.sole@tecn.upf.es

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2003

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Abstract

We present a new method, based on curve evolution, for the reconstruction of a 3D curve from two different projections. It is based on the minimization of an energy functional. Following the work on geodesic active contours by Caselles et al. (in Int. Conf. on Pattern Recognition, 1996, Vol. 43, pp. 693–737), we then transform the problem of minimizing the functional into a problem of geodesic computation in a Riemann space. The Euler-Lagrange equation of this new functional is derived and its associated PDE is solved using the level set formulation, giving the existence and uniqueness results. We apply the model to the reconstruction of a vessel from a biplane angiography.