Globally Optimal Cortical Surface Matching With Exact Landmark Correspondence

Abstract : We present a method for establishing correspondences be- tween human cortical surfaces that exactly matches the positions of given point landmarks, while attaining the global minimum of an ob- jective function that quantifies how far the mapping deviates from con- formality. 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 plau- sibility: 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 spher- ical domain to show that sacrificing exact conformality of the mapping does not cause noticeable reductions in biological plausibility.
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  • HAL Id : hal-00974838, version 1

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Alex Tsui, Devin Fenton, Phong Vuong, Joel Hass, Patrice Koehl, et al.. Globally Optimal Cortical Surface Matching With Exact Landmark Correspondence. Information Processing in Medical Imaging, Jun 2013, Asilomar, California, United States. pp.487-498. ⟨hal-00974838⟩

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