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Vesicles and Amoebae: On Globally Constrained Shape Deformation

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Abstract

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.

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Authors and Affiliations

  1. Center for Intelligent Systems, Computer Science Department, Technion, I.I.T., Haifa, Israel

    Ishay Goldin & Alfred M. Bruckstein

  2. IBISC Laboratory (Computer science, Integrative Biology and Complex Systems), Evry University, 91025, Evry, France

    Jean-Marc Delosme

Authors
  1. Ishay Goldin
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  2. Jean-Marc Delosme
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  3. Alfred M. Bruckstein
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Corresponding author

Correspondence to Ishay Goldin.

Additional information

This research was partially supported by The Center for Complexity Science (CCS) No. 2006-70.

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Goldin, I., Delosme, JM. & Bruckstein, A.M. Vesicles and Amoebae: On Globally Constrained Shape Deformation. J Math Imaging Vis 37, 112–131 (2010). https://doi.org/10.1007/s10851-010-0196-4

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  • DOI: https://doi.org/10.1007/s10851-010-0196-4

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