Brain Surface Conformal Parameterization With the Ricci Flow
作者： Yalin Wang , Jie Shi , Xiaotian Yin , Xianfeng Gu , Tony F. Chan
关键词: Mathematical analysis 、 Mathematics 、 Ricci flow 、 Curvature 、 Surface (mathematics) 、 Boundary (topology) 、 Gaussian curvature 、 Geometry 、 Gaussian 、 Manifold 、 Conformal map
摘要: In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons anatomy, surface-based registration, and signal processing. Here, we introduce the theories continuous discrete Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities they intrinsic stable. First, convert a cortical model into multiple boundary by cutting along selected anatomical landmark curves. Secondly, conformally parameterize each to parameter domain user-designed curvature arrangement. domain, shape index based invariants is computed, inter-subject matching performed solving constrained harmonic map. We illustrate various target arrangements demonstrate stability method using longitudinal data. To map differences in morphometry, studied asymmetry 14 healthy control subjects. used manifold version Hotelling's T2 test, applied Jacobian matrices parameterizations. A permutation cumulative distribution p-values, were estimate overall significance differences. results show our algorithm's power detect subtle group surfaces.
elsevier.com
sci-hub.se 参考文章(82)
Jay N. Giedd, Arthur W. Toga, Roger P. Woods, Paul Thompson, Alan C. Evans, David MacDonald, GROWTH PATTERNS IN THE DEVELOPING HUMAN BRAIN DETECTED USING CONTINUUM-MECHANICAL TENSOR MAPPING ,(1999)
Paul M. Thompson, Michael S. Mega, Christine Vidal, Judith L. Rapoport, Arthur W. Toga, Detecting Disease-Specific Patterns of Brain Structure Using Cortical Pattern Matching and a Population-Based Probabilistic Brain Atlas information processing in medical imaging. ,vol. 2082, pp. 488- 501 ,(2001) , 10.1007/3-540-45729-1_52
Chad D. Abernathey, 道夫 小野, Stefan Kubik, Atlas of the cerebral sulci G. Thieme Verlag , Thieme Medical Publishers. ,(1990)
Anqi Qiu, Michael I. Miller, Cortical hemisphere registration via large deformation diffeomorphic metric curve mapping medical image computing and computer assisted intervention. ,vol. 10, pp. 186- 193 ,(2007) , 10.1007/978-3-540-75757-3_23
Yalin Wang, Xianfeng Gu, Tony F. Chan, Paul M. Thompson, Shing-Tung Yau, Conformal Slit Mapping and Its Applications to Brain Surface Parameterization Medical Image Computing and Computer-Assisted Intervention – MICCAI 2008. ,vol. 11, pp. 585- 593 ,(2008) , 10.1007/978-3-540-85988-8_70
Richard S. Hamilton, Three-manifolds with positive Ricci curvature Journal of Differential Geometry. ,vol. 17, pp. 255- 306 ,(1982) , 10.4310/JDG/1214436922
Yalin Wang, Ming-Chang Chiang, Paul M. Thompson, Automated Surface Matching Using Mutual Information Applied to Riemann Surface Structures Lecture Notes in Computer Science. ,vol. 8, pp. 666- 674 ,(2005) , 10.1007/11566489_82
Steven H. Weintraub, Differential Forms: A Complement to Vector Calculus ,(1997)
Marc Vaillant, Joan Glaunès, Surface matching via currents information processing in medical imaging. ,vol. 19, pp. 381- 392 ,(2005) , 10.1007/11505730_32
Guillaume Auzias, Joan Glaunès, Olivier Colliot, Matthieu Perrot, Jean-François Mangin, Alain Trouvé, Sylvain Baillet, DISCO: A Coherent Diffeomorphic Framework for Brain Registration under Exhaustive Sulcal Constraints Medical Image Computing and Computer-Assisted Intervention – MICCAI 2009. ,vol. 12, pp. 730- 738 ,(2009) , 10.1007/978-3-642-04268-3_90