On concise 3-D simple point characterizations: A marching cubes paradigm

Adam Huang, Hon Man Liu, Chung Wei Lee, Chung Yi Yang, Yuk Ming Tsang

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


The centerlines of tubular structures are useful for medical image visualization and computer-aided diagnosis applications. They can be effectively extracted by using a thinning algorithm that erodes an object layer by layer until only a skeleton is left. An object point is "simple" and can be safely deleted only if the resultant image is topologically equivalent to the original. Numerous characterizations of 3-D simple points based on digital topology already exist. However, little work has been done in the context of marching cubes (MC). This paper reviews several concise 3-D simple point characterizations in a MC paradigm. By using the Euler characteristic and a few newly observed properties in the context of connectivity-consistent MC, we present concise and more self-explanatory proofs. We also present an efficient method for computing the Euler characteristic locally for MC surfaces. Performance evaluations on different implementations are conducted on synthetic data and multidetector computed tomography examination of virtual colonoscopy and angiography.

Original languageEnglish
Article number4530645
Pages (from-to)43-51
Number of pages9
JournalIEEE Transactions on Medical Imaging
Issue number1
StatePublished - Jan 2009


  • Centerline
  • Computed tomography (CT) angiography
  • Computed tomography (CT) colonography
  • Marching cubes
  • Simple point
  • Topological thinning


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