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Pose Invariant Shape Prior Segmentation Using Continuous Cuts and Gradient Descent on Lie Groups

  • Conference paper
Scale Space and Variational Methods in Computer Vision (SSVM 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5567))

Abstract

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.

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© 2009 Springer-Verlag Berlin Heidelberg

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Overgaard, N.C., Fundana, K., Heyden, A. (2009). Pose Invariant Shape Prior Segmentation Using Continuous Cuts and Gradient Descent on Lie Groups. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_57

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  • DOI: https://doi.org/10.1007/978-3-642-02256-2_57

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02255-5

  • Online ISBN: 978-3-642-02256-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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