Conformal Geometry and Brain Flattening
MICCAI '99 Proceedings of the Second International Conference on Medical Image Computing and Computer-Assisted Intervention
Mutual Information-Based 3D Surface Matching with Applications to Face Recognition and Brain Mapping
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
Conformal Slit Mapping and Its Applications to Brain Surface Parameterization
MICCAI '08 Proceedings of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I
Multivariate Tensor-Based Brain Anatomical Surface Morphometry via Holomorphic One-Forms
MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part I
Brain surface conformal parameterization with algebraic functions
MICCAI'06 Proceedings of the 9th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
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In this paper, we introduce theories and algorithms in conformal geometry, including Riemann surface, harmonic map, holomorphic 1-form, and Ricci flow, which play important roles in computational anatomy. In order to study the deformation of brain surfaces, we introduce the multivariate tensor-based morphometry (MTBM) method for statistical computing. For application, we introduce our system for detecting Alzheimer's Disease (AD) symptoms on hippocampal surfaces with an automated surface fluid registration method, which is based on surface conformal mapping and mutual information regularized image fluid registration. Since conformal mappings are diffeomorphic and the mutual information method is able to drive a diffeomorphic flow that is adjusted to enforce appropriate surface correspondences in the surface parameter domain, combining conformal and fluid mappings will generate 3D shape correspondences that are diffeomorphic. We also incorporate in the system a novel method to compute curvatures using surface conformal parameterization. Experimental results in ADNI baseline data diagnostic group difference and APOE4 effects show that our system has better performance than other similar work in the literature.