Human Brain Mapping with Conformal Geometry and Multivariate Tensor-Based Morphometry
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.
KeywordsConformal Mapping Ricci Flow Circle Packing Conformal Geometry Human Brain Mapping
Unable to display preview. Download preview PDF.
- 12.Lepore, N., Brun, C.A., Chiang, M.-C., Chou, Y.-Y., Dutton, R.A., Hayashi, K.M., Lopez, O.L., Aizenstein, H.J., Toga, A.W., Becker, J.T., Thompson, P.M.: Multivariate statistics of the jacobian matrices in tensor based morphometry and their application to HIV/AIDS. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4190, pp. 191–198. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 16.Wang, Y., et al.: Mutual information-based 3D surface matching with applications to face recognition and brain mapping. In: Proc. Intl Conf. Computer Vision, pp. 527–534 (2005)Google Scholar
- 20.Wang, Y., Chan, T.F., Toga, A.W., Thompson, P.M.: Multivariate tensor-based brain anatomical surface morphometry via holomorphic one-forms. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009. LNCS, vol. 5761, pp. 337–344. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 21.Wang, Y.: Multivariate tensor-based subcortical morphometry system (2011), http://gsl.lab.asu.edu/conformal.htm
- 22.Wang, Y., et al.: MRI-based biomarker detection using conformal slit maps and machine learning. In: 16th Annual Meeting of the Organization for Human Brain Mapping (2010)Google Scholar