An Efficient Lagrangian Algorithm for an Anisotropic Geodesic Active Contour Model

  • Günay DoğanEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10302)


We propose an efficient algorithm to minimize an anisotropic surface energy generalizing the Geodesic Active Contour model for image segmentation. In this energy, the weight function may depend on the normal of the curve/surface. Our algorithm is Lagrangian, but nonparametric. We only use the node and connectivity information for computations. Our approach provides a flexible scheme, in the sense that it allows to easily incorporate the generalized gradients proposed recently, especially those based on the \(H^1\) scalar product on the surface. However, unlike these approaches, our scheme is applicable in any number of dimensions, such as surfaces in 3d or 4d, and allows weighted \(H^1\) scalar products, with weights may depending on the normal and the curvature. We derive the second shape derivative of the anisotropic surface energy, and use it as the basis for a new weighted \(H^1\) scalar product. In this way, we obtain a Newton-type method that not only gives smoother flows, but also converges in fewer iterations and much shorter time.


Minimization Algorithm Velocity Equation Shape Derivative Geodesic Active Contour Shape Gradient 
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.



This work was performed under the financial assistance award 70NANB16H306 from the U.S. Department of Commerce, National Institute of Standards and Technology.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Theiss ResearchLa JollaUSA
  2. 2.National Institute of Standards and TechnologyGaithersburgUSA

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