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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 constrainedoptimization problem and pioneer the use of an $L_1$ penalty term to obtainsparse (localized) solutions. In this context, the notion corresponding tosparsity is compact support which entails spatially localized solutions. Wepropose to enforce such a compact support structure by a variationaloptimization formulation with an $L_p$ penalization term, with $0<p<1$. Thechallenging solution of the orthogonality constrained non-convex minimizationproblem is obtained by applying splitting strategies and an ADMM-basediterative algorithm. The effectiveness of the novel compact support basis isdemonstrated in the solution of the 2-manifold decomposition problem whichplays an important role in shape geometry processing where the boundary of a 3Dobject is well represented by a polygonal mesh. We propose an algorithm formesh segmentation and patch-based partitioning (where a genus-0 surfacepatching is required). Experiments on shape partitioning are conducted tovalidate the performance of the proposed compact support basis.

Shape Partitioning via L$_p$ Compressed Modes