TY - GEN
T1 - Hyperbolic Ricci flow and its application in studying lateral ventricle morphometry
AU - Shi, Jie
AU - Thompson, Paul M.
AU - Wang, Yalin
PY - 2012
Y1 - 2012
N2 - Here we propose a novel method to compute surface hyperbolic parameterization for studying brain morphology with the Ricci flow method. Two surfaces are conformally equivalent if there exists a bijective angle-preserving map between them. The Teichmüller space for surfaces with the same topology is a finite-dimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the identity map. A shape index can be defined based on Teichmüller space coordinates, and this shape index is intrinsic and invariant under scaling, translation, rotation, general isometric deformation, and conformal deformation. Using the Ricci flow method, we can conformally map a surface with a negative Euler number to the Poincaré disk and the Teichmüller space coordinates can be computed by geodesic lengths under hyperbolic metric. For lateral ventricular surface registration, we further convert the parameterization to the Klein model where a convex polygon is guaranteed for a multiply connected surface. With the Klein model, diffeomorphisms between lateral ventricular surfaces can be computed with some well known surface registration methods. Compared with prior work, the parameterization does not have any singularities and the intrinsic parameterizations help shape indexing and surface registration. Our preliminary experimental results showed its great promise for analyzing anatomical surface morphology.
AB - Here we propose a novel method to compute surface hyperbolic parameterization for studying brain morphology with the Ricci flow method. Two surfaces are conformally equivalent if there exists a bijective angle-preserving map between them. The Teichmüller space for surfaces with the same topology is a finite-dimensional manifold, where each point represents a conformal equivalence class, and the conformal map is homotopic to the identity map. A shape index can be defined based on Teichmüller space coordinates, and this shape index is intrinsic and invariant under scaling, translation, rotation, general isometric deformation, and conformal deformation. Using the Ricci flow method, we can conformally map a surface with a negative Euler number to the Poincaré disk and the Teichmüller space coordinates can be computed by geodesic lengths under hyperbolic metric. For lateral ventricular surface registration, we further convert the parameterization to the Klein model where a convex polygon is guaranteed for a multiply connected surface. With the Klein model, diffeomorphisms between lateral ventricular surfaces can be computed with some well known surface registration methods. Compared with prior work, the parameterization does not have any singularities and the intrinsic parameterizations help shape indexing and surface registration. Our preliminary experimental results showed its great promise for analyzing anatomical surface morphology.
UR - http://www.scopus.com/inward/record.url?scp=84868235327&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84868235327&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-33530-3_6
DO - 10.1007/978-3-642-33530-3_6
M3 - Conference contribution
AN - SCOPUS:84868235327
SN - 9783642335297
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 61
EP - 76
BT - Multimodal Brain Image Analysis - Second International Workshop, MBIA 2012, Held in Conjunction with MICCAI 2012, Proceedings
T2 - 2nd International Workshop on Multimodal Brain Image Analysis, MBIA 2012, Held in Conjunction with the 15th International Conference on Medical Image Computing and Computer Assisted Intervention, MICCAI 2012
Y2 - 1 October 2012 through 5 October 2012
ER -