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 language | English (US) |
|---|---|
| Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
| Pages | 487-498 |
| Number of pages | 12 |
| Volume | 7917 LNCS |
| DOIs | |
| State | Published - 2013 |
| Event | 23rd International Conference on Information Processing in Medical Imaging, IPMI 2013 - Asilomar, CA, United States Duration: Jun 28 2013 → Jul 3 2013 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 7917 LNCS |
| ISSN (Print) | 03029743 |
| ISSN (Electronic) | 16113349 |
Other
| Other | 23rd International Conference on Information Processing in Medical Imaging, IPMI 2013 |
|---|---|
| Country | United States |
| City | Asilomar, CA |
| Period | 6/28/13 → 7/3/13 |
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ASJC Scopus subject areas
- Computer Science(all)
- Theoretical Computer Science
Cite this
Globally optimal cortical surface matching with exact landmark correspondence. / Tsui, Alex; Fenton, Devin; Vuong, Phong; Hass, Joel; Koehl, Patrice; Amenta, Nina; Coeurjolly, David; DeCarli, Charles; Carmichael, Owen.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7917 LNCS 2013. p. 487-498 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7917 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Globally optimal cortical surface matching with exact landmark correspondence
AU - Tsui, Alex
AU - Fenton, Devin
AU - Vuong, Phong
AU - Hass, Joel
AU - Koehl, Patrice
AU - Amenta, Nina
AU - Coeurjolly, David
AU - DeCarli, Charles
AU - Carmichael, Owen
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
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U2 - 10.1007/978-3-642-38868-2_41
DO - 10.1007/978-3-642-38868-2_41
M3 - Conference contribution
SN - 9783642388675
VL - 7917 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 487
EP - 498
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ER -