Shape Modeling and Analysis with Entropy-Based Particle Systems

  • Joshua Cates
  • P. Thomas Fletcher
  • Martin Styner
  • Martha Shenton
  • Ross Whitaker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4584)


This paper presents a new method for constructing compact statistical point-based models of ensembles of similar shapes that does not rely on any specific surface parameterization. The method requires very little preprocessing or parameter tuning, and is applicable to a wider range of problems than existing methods, including nonmanifold surfaces and objects of arbitrary topology. The proposed method is to construct a point-based sampling of the shape ensemble that simultaneously maximizes both the geometric accuracy and the statistical simplicity of the model. Surface point samples, which also define the shape-to-shape correspondences, are modeled as sets of dynamic particles that are constrained to lie on a set of implicit surfaces. Sample positions are optimized by gradient descent on an energy function that balances the negative entropy of the distribution on each shape with the positive entropy of the ensemble of shapes. We also extend the method with a curvature-adaptive sampling strategy in order to better approximate the geometry of the objects. This paper presents the formulation; several synthetic examples in two and three dimensions; and an application to the statistical shape analysis of the caudate and hippocampus brain structures from two clinical studies.


Particle Method Uniform Sampling Minimum Description Length Implicit Surface Segmented Volume 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Joshua Cates
    • 1
  • P. Thomas Fletcher
    • 1
  • Martin Styner
    • 2
  • Martha Shenton
    • 3
  • Ross Whitaker
    • 1
  1. 1.School of Computing, University of Utah, Salt Lake City UTUSA
  2. 2.Departments of Computer Science and Psychiatry, University of North Carolina at Chapel Hill, Chapel Hill NCUSA
  3. 3.Psychiatry Neuroimaging Laboratory, Brigham and Women’s Hospital, Harvard Medical School; and Laboratory of Neuroscience, VA Boston Healthcare System, Brockton MAUSA

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