Brain anatomical feature detection by solving partial differential equations on general manifolds

Lok Ming Lui, Yalin Wang, Tony F. Chan, Paul M. Thompson

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

One important problem in human brain mapping research is to locate the important anatomical features. Anatomical features on the cortical surface are usually represented by landmark curves, called sulci/gyri curves. These landmark curves are important information for neuroscientists to study brain disease and to match different cortical surfaces. Manual labelling of these landmark curves is time-consuming, especially when large sets of data have to be analyzed. In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an algorithm to obtain a hypothesized landmark region/curves using the Chan-Vese segmentation method, which solves a Partial Differential Equation (PDE) on a manifold with global conformal parameterization. This is done by segmentating the high mean curvature region. Second, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its principal direction field, using umbilic points of the surface as anchors. The landmark curves can then be mapped back onto the cortical surface. Experimental results show that the landmark curves detected by our algorithm closely resemble these manually labeled curves. Next, we applied these automatically labeled landmark curves to generate an optimized conformal parametrization of the cortical surface, in the sense that homologous features across subjects are caused to lie at the same parameter locations in a conformal grid. Experimental results show that our method can effectively help in automatically matching cortical surfaces across subjects.

Original languageEnglish (US)
Pages (from-to)605-618
Number of pages14
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume7
Issue number3
StatePublished - May 2007
Externally publishedYes

Fingerprint

Feature Detection
Partial differential equations
Landmarks
Brain
Partial differential equation
Curve
Parametrization
Principal direction
Brain mapping
Parameterization
Anchors
Labeling
Location Parameter
Experimental Results
Mean Curvature
Tracing
Large Set
Segmentation

Keywords

  • Brain anatomical feature
  • Conformal parametrization
  • Curvature
  • Partial differential equations
  • Variational problem

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

Brain anatomical feature detection by solving partial differential equations on general manifolds. / Lui, Lok Ming; Wang, Yalin; Chan, Tony F.; Thompson, Paul M.

In: Discrete and Continuous Dynamical Systems - Series B, Vol. 7, No. 3, 05.2007, p. 605-618.

Research output: Contribution to journalArticle

@article{9ca77507dd8c46f6a7b9636136eff097,
title = "Brain anatomical feature detection by solving partial differential equations on general manifolds",
abstract = "One important problem in human brain mapping research is to locate the important anatomical features. Anatomical features on the cortical surface are usually represented by landmark curves, called sulci/gyri curves. These landmark curves are important information for neuroscientists to study brain disease and to match different cortical surfaces. Manual labelling of these landmark curves is time-consuming, especially when large sets of data have to be analyzed. In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an algorithm to obtain a hypothesized landmark region/curves using the Chan-Vese segmentation method, which solves a Partial Differential Equation (PDE) on a manifold with global conformal parameterization. This is done by segmentating the high mean curvature region. Second, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its principal direction field, using umbilic points of the surface as anchors. The landmark curves can then be mapped back onto the cortical surface. Experimental results show that the landmark curves detected by our algorithm closely resemble these manually labeled curves. Next, we applied these automatically labeled landmark curves to generate an optimized conformal parametrization of the cortical surface, in the sense that homologous features across subjects are caused to lie at the same parameter locations in a conformal grid. Experimental results show that our method can effectively help in automatically matching cortical surfaces across subjects.",
keywords = "Brain anatomical feature, Conformal parametrization, Curvature, Partial differential equations, Variational problem",
author = "Lui, {Lok Ming} and Yalin Wang and Chan, {Tony F.} and Thompson, {Paul M.}",
year = "2007",
month = "5",
language = "English (US)",
volume = "7",
pages = "605--618",
journal = "Discrete and Continuous Dynamical Systems - Series B",
issn = "1531-3492",
publisher = "Southwest Missouri State University",
number = "3",

}

TY - JOUR

T1 - Brain anatomical feature detection by solving partial differential equations on general manifolds

AU - Lui, Lok Ming

AU - Wang, Yalin

AU - Chan, Tony F.

AU - Thompson, Paul M.

PY - 2007/5

Y1 - 2007/5

N2 - One important problem in human brain mapping research is to locate the important anatomical features. Anatomical features on the cortical surface are usually represented by landmark curves, called sulci/gyri curves. These landmark curves are important information for neuroscientists to study brain disease and to match different cortical surfaces. Manual labelling of these landmark curves is time-consuming, especially when large sets of data have to be analyzed. In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an algorithm to obtain a hypothesized landmark region/curves using the Chan-Vese segmentation method, which solves a Partial Differential Equation (PDE) on a manifold with global conformal parameterization. This is done by segmentating the high mean curvature region. Second, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its principal direction field, using umbilic points of the surface as anchors. The landmark curves can then be mapped back onto the cortical surface. Experimental results show that the landmark curves detected by our algorithm closely resemble these manually labeled curves. Next, we applied these automatically labeled landmark curves to generate an optimized conformal parametrization of the cortical surface, in the sense that homologous features across subjects are caused to lie at the same parameter locations in a conformal grid. Experimental results show that our method can effectively help in automatically matching cortical surfaces across subjects.

AB - One important problem in human brain mapping research is to locate the important anatomical features. Anatomical features on the cortical surface are usually represented by landmark curves, called sulci/gyri curves. These landmark curves are important information for neuroscientists to study brain disease and to match different cortical surfaces. Manual labelling of these landmark curves is time-consuming, especially when large sets of data have to be analyzed. In this paper, we present algorithms to automatically detect and match landmark curves on cortical surfaces to get an optimized brain conformal parametrization. First, we propose an algorithm to obtain a hypothesized landmark region/curves using the Chan-Vese segmentation method, which solves a Partial Differential Equation (PDE) on a manifold with global conformal parameterization. This is done by segmentating the high mean curvature region. Second, we propose an automatic landmark curve tracing method based on the principal directions of the local Weingarten matrix. Based on the global conformal parametrization of a cortical surface, our method adjusts the landmark curves iteratively on the spherical or rectangular parameter domain of the cortical surface along its principal direction field, using umbilic points of the surface as anchors. The landmark curves can then be mapped back onto the cortical surface. Experimental results show that the landmark curves detected by our algorithm closely resemble these manually labeled curves. Next, we applied these automatically labeled landmark curves to generate an optimized conformal parametrization of the cortical surface, in the sense that homologous features across subjects are caused to lie at the same parameter locations in a conformal grid. Experimental results show that our method can effectively help in automatically matching cortical surfaces across subjects.

KW - Brain anatomical feature

KW - Conformal parametrization

KW - Curvature

KW - Partial differential equations

KW - Variational problem

UR - http://www.scopus.com/inward/record.url?scp=34250796866&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34250796866&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 605

EP - 618

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 3

ER -