Introducing willmore flow into level set segmentation of spinal vertebrae

Poay Hoon Lim*, Ulas Bagci, Li Bai

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Scopus citations


Segmentation of spinal vertebrae in 3-D space is a crucial step in the study of spinal related disease or disorders. However, the complexity of vertebrae shapes, with gaps in the cortical bone and boundaries, as well as noise, inhomogeneity, and incomplete information in images, has made spinal vertebrae segmentation a difficult task. In this paper, we introduce a new method for an accurate spinal vertebrae segmentation that is capable of dealing with noisy images with missing information. This is achieved by introducing an edge-mounted Willmore flow, as well as a prior shape kernel density estimator, to the level set segmentation framework. While the prior shape model provides much needed prior knowledge when information is missing from the image, and draws the level set function toward prior shapes, the edge-mounted Willmore flow helps to capture the local geometry and smoothes the evolving level set surface. Evaluation of the segmentation results with ground-truth validation demonstrates the effectiveness of the proposed approach: an overall accuracy of 89.32±1.70\% and 14.03± 1.40 mm are achieved based on the Dice similarity coefficient and Hausdorff distance, respectively, while the inter-and intraobserver variation agreements are 92.11± 1.97\%, 94.94±1.69\%, 3.32± 0.46, and 3.80±0.56mm.

Original languageEnglish (US)
Article number6336794
Pages (from-to)115-122
Number of pages8
JournalIEEE Transactions on Biomedical Engineering
Issue number1
StatePublished - 2013
Externally publishedYes


  • Kernel density estimation (KDE)
  • Willmore flow
  • level set
  • vertebrae segmentation

ASJC Scopus subject areas

  • Biomedical Engineering


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