Statistics of Pose and Shape in Multi-object Complexes Using Principal Geodesic Analysis

  • Martin Styner
  • Kevin Gorczowski
  • Tom Fletcher
  • Ja Yeon Jeong
  • Stephen M. Pizer
  • Guido Gerig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4091)


A main focus of statistical shape analysis is the description of variability of a population of geometric objects. In this paper, we present work in progress towards modeling the shape and pose variability of sets of multiple objects. Principal geodesic analysis (PGA) is the extension of the standard technique of principal component analysis (PCA) into the nonlinear Riemannian symmetric space of pose and our medial m-rep shape description, a space in which use of PCA would be incorrect. In this paper, we discuss the decoupling of pose and shape in multi-object sets using different normalization settings. Further, we introduce new methods of describing the statistics of object pose using a novel extension of PGA, which previously has been used for global shape statistics. These new pose statistics are then combined with shape statistics to form a more complete description of multi-object complexes. We demonstrate our methods in an application to a longitudinal pediatric autism study with object sets of 10 subcortical structures in a population of 20 subjects. The results show that global scale accounts for most of the major mode of variation across time. Furthermore, the PGA components and the corresponding distribution of different subject groups vary significantly depending on the choice of normalization, which illustrates the importance of global and local pose alignment in multi-object shape analysis.


Independent Component Analysis Shape Space Statistical Shape Modeling Medial Atom Shape Variability 
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-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martin Styner
    • 1
    • 2
  • Kevin Gorczowski
    • 1
  • Tom Fletcher
    • 1
  • Ja Yeon Jeong
    • 1
  • Stephen M. Pizer
    • 1
  • Guido Gerig
    • 1
    • 2
  1. 1.Department of Computer Science 
  2. 2.Department of PsychiatryThe University of North CarolinaChapel Hill

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