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 $L_1$ penalty term to obtain spar...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
20.04.2018
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Subjects | |
Online Access | Get full text |
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Summary: | 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 $L_1$ 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 $L_p$ penalization term, with $0<p<1$. 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. |
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DOI: | 10.48550/arxiv.1804.07620 |