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An Efficient Lagrangian Algorithm for an Anisotropic Geodesic Active Contour Model

Published

Author(s)

Gunay Dogan

Abstract

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.
Proceedings Title
Proceedings of the Sixth International Conference on Scale Space and Variational Methods in
Computer Vision
Volume
10302
Conference Dates
June 4-8, 2017
Conference Location
Kolding
Conference Title
Sixth International Conference on Scale Space and Variational Methods in Computer Vision

Keywords

active contours, image segmentation, shape optimization, shape derivatives

Citation

Dogan, G. (2017), An Efficient Lagrangian Algorithm for an Anisotropic Geodesic Active Contour Model, Proceedings of the Sixth International Conference on Scale Space and Variational Methods in Computer Vision, Kolding, -1, [online], https://doi.org/10.1007/978-3-319-58771-4_33 (Accessed May 21, 2022)
Created May 17, 2017, Updated September 18, 2020