Journal of Mathematical Imaging and Vision

, Volume 27, Issue 3, pp 217–229 | Cite as

Anisotropic Curvature Motion for Structure Enhancing Smoothing of 3D MR Angiography Data

  • Oliver NemitzEmail author
  • Martin Rumpf
  • Tolga Tasdizen
  • Ross Whitaker


We propose a novel concept of shape prior for the processing of tubular structures in 3D images. It is based on the notion of an anisotropic area energy and the corresponding geometric gradient flow. The anisotropic area functional incorporates a locally adapted template as a shape prior for tubular vessel structures consisting of elongated, ellipsoidal shape models. The gradient flow for this functional leads to an anisotropic curvature motion model, where the evolution is driven locally in direction of the considered template. The problem is formulated in a level set framework, and a stable and robust method for the identification of the local prior is presented. The resulting algorithm is able to smooth the vessels, pushing solution toward elongated cylinders with round cross sections, while bridging gaps in the underlying raw data. The implementation includes a finite-element scheme for numerical accuracy and a narrow band strategy for computational efficiency.


anisotropic mean curvature motion denoising and reconstruction local classification 


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Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  • Oliver Nemitz
    • 1
    Email author
  • Martin Rumpf
    • 1
  • Tolga Tasdizen
    • 2
  • Ross Whitaker
    • 2
  1. 1.Institut für Numerische SimulationRheinische Friedrich-Wilhelms-Universität BonnBonnGermany
  2. 2.3450 Merrill Engineering Building, School of ComputingUniversity of UtahSalt Lake City

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