13 research outputs found
Global-Mode Analysis of Full-Disk Data from the Michelson Doppler Imager and the Helioseismic and Magnetic Imager
Spontaneous flux concentrations from the negative effective magnetic pressure instability beneath a radiative stellar surface
Shape Partitioning via L p Compressed Modes
The eigenfunctions of the Laplace Beltrami operator (Manifold Harmonics)
define a function basis that can be used in spectral analysis on manifolds. In
[21] the authors recast the problem as an orthogonality constrained
optimization problem and pioneer the use of an penalty term to obtain
sparse (localized) solutions. In this context, the notion corresponding to
sparsity is compact support which entails spatially localized solutions. We
propose to enforce such a compact support structure by a variational
optimization formulation with an penalization term, with . The
challenging solution of the orthogonality constrained non-convex minimization
problem is obtained by applying splitting strategies and an ADMM-based
iterative algorithm. The effectiveness of the novel compact support basis is
demonstrated in the solution of the 2-manifold decomposition problem which
plays an important role in shape geometry processing where the boundary of a 3D
object is well represented by a polygonal mesh. We propose an algorithm for
mesh segmentation and patch-based partitioning (where a genus-0 surface
patching is required). Experiments on shape partitioning are conducted to
validate the performance of the proposed compact support basis