Brain anatomical feature detection by solving partial differential equations on general manifolds

Lok Ming Lui*, Yalin Wang, Tony F. Chan, Paul M. Thompson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


One important problem in human brain mapping research is to locate the important anatomical features. Anatomical features on the cortical surface are usually represented by landmark curves, called sulci/gyri curves. These landmark curves are important information for neuroscientists to study brain disease and to match different cortical surfaces. Manual labelling of these landmark curves is time-consuming, especially when large sets of data have to be analyzed. In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an algorithm to obtain a hypothesized landmark region/curves using the Chan-Vese segmentation method, which solves a Partial Differential Equation (PDE) on a manifold with global conformal parameterization. This is done by segmentating the high mean curvature region. Second, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its principal direction field, using umbilic points of the surface as anchors. The landmark curves can then be mapped back onto the cortical surface. Experimental results show that the landmark curves detected by our algorithm closely resemble these manually labeled curves. Next, we applied these automatically labeled landmark curves to generate an optimized conformal parametrization of the cortical surface, in the sense that homologous features across subjects are caused to lie at the same parameter locations in a conformal grid. Experimental results show that our method can effectively help in automatically matching cortical surfaces across subjects.

Original languageEnglish (US)
Pages (from-to)605-618
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Issue number3
StatePublished - May 2007
Externally publishedYes


  • Brain anatomical feature
  • Conformal parametrization
  • Curvature
  • Partial differential equations
  • Variational problem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Brain anatomical feature detection by solving partial differential equations on general manifolds'. Together they form a unique fingerprint.

Cite this