This paper proposes a novel formulation of the Chan-Vese model for pose invariant shape prior segmentation as a continuous cut problem. The model is based on the classic L 2 shape dissimilarity measure and with pose invariance under the full (Lie-) group of similarity transforms in the plane. To overcome the common numerical problems associated with step size control for translation, rotation and scaling in the discretization of the pose model, a new gradient descent procedure for the pose estimation is introduced. This procedure is based on the construction of a Riemannian structure on the group of transformations and a derivation of the corresponding pose energy gradient. Numerically, this amounts to an adaptive step size selection in the discretization of the gradient descent equations. Together with efficient numerics for TV-minimization we get a fast and reliable implementation of the model. Moreover, the theory introduced is generic and reliable enough for application to more general segmentation- and shape-models. © 2009 Springer Berlin Heidelberg.
CITATION STYLE
Overgaard, N. C., Fundana, K., & Heyden, A. (2009). Pose invariant shape prior segmentation using continuous cuts and gradient descent on lie groups. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5567 LNCS, pp. 684–695). https://doi.org/10.1007/978-3-642-02256-2_57
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