Estimation of Smooth Growth Trajectories with Controlled Acceleration from Time Series Shape Data

  • James Fishbaugh
  • Stanley Durrleman
  • Guido Gerig
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6892)


Longitudinal shape analysis often relies on the estimation of a realistic continuous growth scenario from data sparsely distributed in time. In this paper, we propose a new type of growth model parameterized by acceleration, whereas standard methods typically control the velocity. This mimics the behavior of biological tissue as a mechanical system driven by external forces. The growth trajectories are estimated as smooth flows of deformations, which are twice differentiable. This differs from piecewise geodesic regression, for which the velocity may be discontinuous. We evaluate our approach on a set of anatomical structures of the same subject, scanned 16 times between 4 and 8 years of age. We show our acceleration based method estimates smooth growth, demonstrating improved regularity compared to piecewise geodesic regression. Leave-several-out experiments show that our method is robust to missing observations, as well as being less sensitive to noise, and is therefore more likely to capture the underlying biological growth.


Growth Model Growth Trajectory Target Shape Kernel Regression Intracranial Volume 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • James Fishbaugh
    • 1
  • Stanley Durrleman
    • 1
  • Guido Gerig
    • 1
  1. 1.Scientific Computing and Imaging InstituteUniversity of UtahSalt Lake CityUSA

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