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Wulff Shapes at Zero Temperature for Some Models Used in Image Processing

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Statistics and Analysis of Shapes

Abstract

In this chapter, we study isotropic properties of some Gibbs fields used for image segmentation. We consider ferromagnetic models defined by 3 × 3 interactions. We compute the Wulff shape of these models at zero temperature. A classification of the considered models with respect to this shape is given. We also give some conjectures which provide conditions necessary to obtain a regular shape. Finally, the influence of the Wulff shape of a given model is shown on real data in the context of magnetic resonance image segmentation.

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© 2006 Birkhäuser Boston

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Descombes, X., Pechersky, E. (2006). Wulff Shapes at Zero Temperature for Some Models Used in Image Processing. In: Krim, H., Yezzi, A. (eds) Statistics and Analysis of Shapes. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4481-4_11

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