Globally optimal cortical surface matching with exact landmark correspondence

Alex Tsui, Devin Fenton, Phong Vuong, Joel Hass, Patrice Koehl, Nina Amenta, David Coeurjolly, Charles DeCarli, Owen Carmichael

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

Abstract

We present a method for establishing correspondences between human cortical surfaces that exactly matches the positions of given point landmarks, while attaining the global minimum of an objective function that quantifies how far the mapping deviates from conformality. On each surface, a conformal transformation is applied to the Euclidean distance metric, resulting in a hyperbolic metric with isolated cone point singularities at the landmarks. Equivalently, each surface is mapped to a hyperbolic orbifold: a pillow-like surface with each point landmark corresponding to a pillow corner. An initial surface-to-surface mapping exactly aligns the landmarks, and gradient descent is used to find the single, global minimum of the Dirichlet energy of the remainder of the mapping. Using a population of real MRI-based cortical surfaces with manually labeled sulcus endpoints as landmarks, we evaluate the approach by how much it distorts surfaces and by its biological plausibility: how well it aligns previously-unseen anatomical landmarks and by how well it promotes expected associations between cortical thickness and age. We show that, compared to a painstakingly-tuned approach that balances a tradeoff between minimizing landmark mismatch and Dirichlet energy, our method has similar biological plausibility, superior surface distortion, a better theoretical foundation, and fewer arbitrary parameters to tune. We also compare to conformal mapper in the spherical domain to show that sacrificing exact conformality of the mapping does not cause noticeable reductions in biological plausibility.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages487-498
Number of pages12
Volume7917 LNCS
DOIs
StatePublished - 2013
Event23rd International Conference on Information Processing in Medical Imaging, IPMI 2013 - Asilomar, CA, United States
Duration: Jun 28 2013Jul 3 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7917 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other23rd International Conference on Information Processing in Medical Imaging, IPMI 2013
CountryUnited States
CityAsilomar, CA
Period6/28/137/3/13

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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Tsui, A., Fenton, D., Vuong, P., Hass, J., Koehl, P., Amenta, N., Coeurjolly, D., DeCarli, C., & Carmichael, O. (2013). Globally optimal cortical surface matching with exact landmark correspondence. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7917 LNCS, pp. 487-498). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7917 LNCS). https://doi.org/10.1007/978-3-642-38868-2_41