Hyperbolic Ricci flow and its application in studying lateral ventricle morphometry

Jie Shi, Paul M. Thompson, Yalin Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

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.

Original languageEnglish (US)
Title of host publicationMultimodal Brain Image Analysis - Second International Workshop, MBIA 2012, Held in Conjunction with MICCAI 2012, Proceedings
Pages61-76
Number of pages16
DOIs
StatePublished - Nov 6 2012
Event2nd 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 - Nice, France
Duration: Oct 1 2012Oct 5 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7509 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd 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
CountryFrance
CityNice
Period10/1/1210/5/12

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Shi, J., Thompson, P. M., & Wang, Y. (2012). Hyperbolic Ricci flow and its application in studying lateral ventricle morphometry. In Multimodal Brain Image Analysis - Second International Workshop, MBIA 2012, Held in Conjunction with MICCAI 2012, Proceedings (pp. 61-76). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7509 LNCS). https://doi.org/10.1007/978-3-642-33530-3_6