Vessels as 4-D curves: Global minimal 4-D paths to extract 3-D tubular surfaces and centerlines

Li Hua, Anthony Yezzi

Research output: Contribution to journalArticlepeer-review

166 Scopus citations


In this paper, we propose an innovative approach to the segmentation of tubular structures. This approach combines all of the benefits of minimal path techniques such as global minimizers, fast computation, and powerful incorporation of user input, while also having the capability to represent and detect vessel surfaces directly which so far has been a feature restricted to active contour and surface techniques. The key is to represent the trajectory of a tubular structure not as a 3-D curve but to go up a dimension and represent the entire structure as a 4-D curve. Then we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied endpoints in order to reconstruct tubular structures from noisy or low contrast 3-D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3-D minimal path techniques, however, we are able to represent a full tubular surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a tube's "central curve." We demonstrate and validate the utility of this approach on magnetic resonance (MR) angiography and computed tomography (CT) images of coronary arteries.

Original languageEnglish
Pages (from-to)1213-1223
Number of pages11
JournalIEEE Transactions on Medical Imaging
Issue number9
StatePublished - Sep 2007


  • Eikonal equations
  • Fast marching techniques
  • Geodesic active contours
  • Global minima
  • Minimal path methods


Dive into the research topics of 'Vessels as 4-D curves: Global minimal 4-D paths to extract 3-D tubular surfaces and centerlines'. Together they form a unique fingerprint.

Cite this