An Efficient Lagrangian Algorithm for an Anisotropic Geodesic Active Contour Model
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.
KeywordsMinimization Algorithm Velocity Equation Shape Derivative Geodesic Active Contour Shape Gradient
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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