Estimating topology preserving and smooth displacement fields

Bilge Karaçali, Christos Davatzikos

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


We propose a method for enforcing topology preservation and smoothness onto a given displacement field. We first analyze the conditions for topology preservation on two- and three-dimensional displacement fields over a discrete rectangular grid. We then pose the problem of finding the closest topology preserving displacement field in terms of its complete set of gradients, which we later solve using a cyclic projections framework. Adaptive smoothing of a displacement field is then formulated as an extension of topology preservation, via constraints imposed on the Jacobian of the displacement field. The simulation results indicate that this technique is a fast and reliable method to estimate a topology preserving displacement field from a noisy observation that does not necessarily preserve topology. They also show that the proposed smoothing method can render morphometric analysis methods that are based on displacement field of shape transformations more robust to noise without removing important morphologic characteristics.

Original languageEnglish (US)
Pages (from-to)868-880
Number of pages13
JournalIEEE transactions on medical imaging
Issue number7
StatePublished - Jul 2004
Externally publishedYes

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Computer Science Applications
  • Electrical and Electronic Engineering


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