Compressed Manifold Modes for Mesh Processing - implementation -

Kiran Varanasi mentioned it on the Google+ Community. He also said:

Compressed manifold modes are compressed eigenfunctions of the Laplace-Beltrami operator on 3D manifold surfaces. They constitute a novel functional basis, called the compressed manifold basis, where each function has local support. We derive a method, based on ADMM, for computing compressed manifold modes (CMMs) for discrete polyhedral 3D meshes. We show that CMMs identify key shape features, yielding an intuitive understanding of the basis for a human observer, where a shape can be processed as a collection of parts. We demonstrate various applications in 3D geometry processing. Our paper is published at the Symposium of Geometry Processing (SGP) 2014. We release the source-code for the method.

Please also refer to "Compressed modes for variational problems in mathematics and physics" - Ozolins, Lai, Caflisch & Osher, PNAS 2013.

Prof. Stan Osher's talk on their PNAS paper (and more) can be found here:

http://nuit-blanche.blogspot.fr/2013/08/videos-and-slides-sahd-2013-duke.html

Thanks Kiran ! Here is the paper and attendant implementation:
 

Compressed Manifold Modes for Mesh Processing by Thomas Neumann, Kiran Varanasi, Christian Theobalt, Marcus Magnor, and Markus Wacker

This paper introduces compressed eigenfunctions of the Laplace-Beltrami operator on 3D manifold surfaces. They constitute a novel functional basis, called the compressed manifold basis, where each function has local support. We derive an algorithm, based on the alternating direction method of multipliers (ADMM), to compute this basis on a given triangulated mesh. We show that compressed manifold modes identify key shape features, yielding an intuitive understanding of the basis for a human observer, where a shape can be processed as a collection of parts. We evaluate compressed manifold modes for potential applications in in shape matching and mesh abstraction. Our results show that this basis has distinct advantages over existing alternatives, indicating high potential for a wide range of use-cases in mesh processing.

The project page with implementation is here.

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