Details
| Original language | English |
|---|---|
| Pages (from-to) | 739-755 |
| Number of pages | 17 |
| Journal | CAD Computer Aided Design |
| Volume | 41 |
| Issue number | 10 |
| Early online date | 27 Feb 2009 |
| Publication status | Published - Oct 2009 |
Abstract
This paper proposes the use of the surface-based Laplace-Beltrami and the volumetric Laplace eigenvalues and eigenfunctions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and eigenfunctions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel.
Keywords
- Brain structure, Caudate nucleus, Eigenfunctions, Eigenvalues, Laplace-Beltrami spectra, Morse-Smale complex, Nodal domains, Reeb graph, Schizotypal personality disorder
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
- Engineering(all)
- Industrial and Manufacturing Engineering
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In: CAD Computer Aided Design, Vol. 41, No. 10, 10.2009, p. 739-755.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Laplace-Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis
AU - Reuter, Martin
AU - Wolter, Franz Erich
AU - Shenton, Martha
AU - Niethammer, Marc
PY - 2009/10
Y1 - 2009/10
N2 - This paper proposes the use of the surface-based Laplace-Beltrami and the volumetric Laplace eigenvalues and eigenfunctions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and eigenfunctions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel.
AB - This paper proposes the use of the surface-based Laplace-Beltrami and the volumetric Laplace eigenvalues and eigenfunctions as shape descriptors for the comparison and analysis of shapes. These spectral measures are isometry invariant and therefore allow for shape comparisons with minimal shape pre-processing. In particular, no registration, mapping, or remeshing is necessary. The discriminatory power of the 2D surface and 3D solid methods is demonstrated on a population of female caudate nuclei (a subcortical gray matter structure of the brain, involved in memory function, emotion processing, and learning) of normal control subjects and of subjects with schizotypal personality disorder. The behavior and properties of the Laplace-Beltrami eigenvalues and eigenfunctions are discussed extensively for both the Dirichlet and Neumann boundary condition showing advantages of the Neumann vs. the Dirichlet spectra in 3D. Furthermore, topological analyses employing the Morse-Smale complex (on the surfaces) and the Reeb graph (in the solids) are performed on selected eigenfunctions, yielding shape descriptors, that are capable of localizing geometric properties and detecting shape differences by indirectly registering topological features such as critical points, level sets and integral lines of the gradient field across subjects. The use of these topological features of the Laplace-Beltrami eigenfunctions in 2D and 3D for statistical shape analysis is novel.
KW - Brain structure
KW - Caudate nucleus
KW - Eigenfunctions
KW - Eigenvalues
KW - Laplace-Beltrami spectra
KW - Morse-Smale complex
KW - Nodal domains
KW - Reeb graph
KW - Schizotypal personality disorder
UR - http://www.scopus.com/inward/record.url?scp=69849109283&partnerID=8YFLogxK
U2 - 10.1016/j.cad.2009.02.007
DO - 10.1016/j.cad.2009.02.007
M3 - Article
AN - SCOPUS:69849109283
VL - 41
SP - 739
EP - 755
JO - CAD Computer Aided Design
JF - CAD Computer Aided Design
SN - 0010-4485
IS - 10
ER -