Journal of Mathematical Imaging and Vision

, Volume 37, Issue 2, pp 112–131 | Cite as

Vesicles and Amoebae: On Globally Constrained Shape Deformation

  • Ishay Goldin
  • Jean-Marc Delosme
  • Alfred M. Bruckstein


Modeling the deformation of shapes under constraints on both perimeter and area is a challenging task due to the highly nontrivial interaction between the need for flexible local rules for manipulating the boundary and the global constraints. We propose several methods to address this problem and generate “random walks” in the space of shapes obeying quite general possibly time varying constraints on their perimeter and area. Design of perimeter and area preserving deformations are an interesting and useful special case of this problem. The resulting deformation models are employed in annealing processes that evolve original shapes toward shapes that are optimal in terms of boundary bending-energy or other functionals. Furthermore, such models may find applications in the analysis of sequences of real images of deforming objects obeying global constraints as building blocks for registration and tracking algorithms.


Constrained shape evolution Constant shape-factor deformations Amoeba motion Vesicles 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Ishay Goldin
    • 1
  • Jean-Marc Delosme
    • 2
  • Alfred M. Bruckstein
    • 1
  1. 1.Center for Intelligent Systems, Computer Science DepartmentTechnion, I.I.T.HaifaIsrael
  2. 2.IBISC Laboratory (Computer science, Integrative Biology and Complex Systems)Evry UniversityEvryFrance

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