Deformable Modeling Using a 3D Boundary Representation with Quadratic Constraints on the Branching Structure of the Blum Skeleton

  • Paul A. Yushkevich
  • Hui Gary Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7917)


We propose a new approach for statistical shape analysis of 3D anatomical objects based on features extracted from skeletons. Like prior work on medial representations [7,15,9], the approach involves deforming a template to target shapes in a way that preserves the branching structure of the skeleton and provides intersubject correspondence. However, unlike medial representations, which parameterize the skeleton surfaces explicitly, our representation is boundary-centric, and the skeleton is implicit. Similar to prior constrained modeling methods developed 2D objects [8] or tube-like 3D objects [13], we impose symmetry constraints on tuples of boundary points in a way that guarantees the preservation of the skeleton’s topology under deformation. Once discretized, the problem of deforming a template to a target shape is formulated as a quadratically constrained quadratic programming problem. The new technique is evaluated in terms of its ability to capture the shape of the corpus callosum tract extracted from diffusion-weighted MRI.


Corpus Callosum Target Object Medial Axis Subdivision Scheme Iterative Close Point 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Paul A. Yushkevich
    • 1
  • Hui Gary Zhang
    • 2
  1. 1.Penn Image Computing and Science Laboratory (PICSL), Department of RadiologyUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Centre for Medical Image Computing, Department of Computer ScienceUniversity College LondonLondonUnited Kingdom

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