Metric optimization for surface analysis in the Laplace-Beltrami embedding space

Yonggang Shi*, Rongjie Lai, Danny J.J. Wang, Daniel Pelletier, David Mohr, Nancy Sicotte, Arthur W. Toga

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


In this paper, we present a novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research. Using the Laplace-Beltrami eigen-system, we represent each surface with an isometry invariant embedding in a high dimensional space. The key idea in our system is that we realize surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding. By minimizing a distance measure in the embedding space with metric optimization, our method generates a conformal map directly between surfaces with highly uniform metric distortion and the ability of aligning salient geometric features. Besides pairwise surface maps, we also extend the metric optimization approach for group-wise atlas construction and multi-atlas cortical label fusion. In experimental results, we demonstrate the robustness and generality of our method by applying it to map both cortical and hippocampal surfaces in population studies. For cortical labeling, our method achieves excellent performance in a cross-validation experiment with 40 manually labeled surfaces, and successfully models localized brain development in a pediatric study of 80 subjects. For hippocampal mapping, our method produces much more significant results than two popular tools on a multiple sclerosis study of 109 subjects.

Original languageEnglish (US)
Article number6778058
Pages (from-to)1447-1463
Number of pages17
JournalIEEE Transactions on Medical Imaging
Issue number7
StatePublished - Jul 2014


  • Cortex
  • Laplace-Beltrami embedding
  • hippocampus
  • metric optimization
  • surface mapping

ASJC Scopus subject areas

  • Software
  • Radiological and Ultrasound Technology
  • Electrical and Electronic Engineering
  • Computer Science Applications


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