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

Hua Li, Anthony Yezzi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

16 Scopus citations

Abstract

In this paper, we propose an innovative approach to the segmentation of tubular or vessel-like structures which combines all the benefits of minimal path techniques (global minimizers, fast computation, powerful incorporation of user input) with some of the benefits of active surface techniques (representation of a full 3D tubular surface rather than a just curve). The key is to represent the trajectory of the vessel not as a 3D curve but to go up a dimension and represent the entire vessel as a 4D curve, where each 4D point represents a 3D sphere (three coordinates for the center point and one for the radius). The 3D vessel structure is then obtained as the envelope of the family of spheres traversed along this 4D curve. Because the 3D surface is simply a curve in 4D, we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied end-points in order to reconstruct vessels from noisy or low contrast 3D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3D minimal path techniques, however, we are able to represent the full vessel surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a vessel's "central curve", which is obtained by tracing the center points of the family of 3D spheres rather than its envelope. We demonstrate the utility of this approach on 2D images of roads as well as both 2D and 3D MR angiography and CT .

Original languageEnglish
Title of host publication2006 Conference on Computer Vision and Pattern Recognition Workshop
DOIs
StatePublished - Dec 21 2006
Event2006 Conference on Computer Vision and Pattern Recognition Workshops - New York, NY, United States
Duration: Jun 17 2006Jun 22 2006

Publication series

NameProceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Volume2006
ISSN (Print)1063-6919

Conference

Conference2006 Conference on Computer Vision and Pattern Recognition Workshops
CountryUnited States
CityNew York, NY
Period06/17/0606/22/06

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    Li, H., & Yezzi, A. (2006). Vessels as 4D curves: Global minimal 4D paths to extract 3D tubular surfaces. In 2006 Conference on Computer Vision and Pattern Recognition Workshop [1640523] (Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition; Vol. 2006). https://doi.org/10.1109/CVPRW.2006.210