Publikationen nach Jahren
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Artikel:
1.
,
"Laplace-Beltrami Eigenvalues and Topological Features of Eigenfunctions for Statistical Shape Analysis
",
Computer Aided Design
41
(2009),
no. 10,
739 - 755,
ftp://ftp.gdv.uni-hannover.de/papers/reuter2009-caudate.pdf
ftp://ftp.gdv.uni-hannover.de/papers/reuter2009-caudate.pdf
This paper proposes the use of the surface based Laplace-Beltrami and the volumetric Laplace eigenvalues and -functions 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 -functions
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.
Beiträge in Tagungsbänden:
2.
,
"Aufbau eines VR-Systems zur multimodalen Interaktion mit komplexen physikalischen Modellen ",
6. Workshop der GI-Fachgruppe VR/AR,
(Andreas Gendt, Marc Erich Latoschik, ed.),
Shaker Verlag,
112009,
p. 49--60,
3.
,
"Analysis of Jump Behavior in Nonlinear Electronic Circuits Using Computational Geometric Methods.",
2nd International Workshop on Nonlinear Dynamics and Synchronization (INDS 2009),
72009,
p. 89-94,
4.
,
"Nonlinear Electric Circuit Analysis from a Differential Geometric Point of View.",
15th edition of the International Symposium on Theoretical Electrical Engineering (ISTET'09),
62009,
p. 169-172,
ISBN: 978-3-8007-3166-4
