Chordal Decomposition for Spectral Coarsening

TL;DR

This paper presents a new spectral coarsening method using chordal decomposition that reduces operator size while maintaining spectral properties, enabling efficient applications in geometry processing.

Contribution

It introduces a convex optimization-based solver for spectral coarsening that balances accuracy and sparsity, with novel applications like volume-to-surface approximation.

Findings

Achieves state-of-the-art spectral coarsening results

Enables mesh-tailored operators for visualization

Supports operator detachment from meshes

Abstract

We introduce a novel solver to significantly reduce the size of a geometric operator while preserving its spectral properties at the lowest frequencies. We use chordal decomposition to formulate a convex optimization problem which allows the user to control the operator sparsity pattern. This allows for a trade-off between the spectral accuracy of the operator and the cost of its application. We efficiently minimize the energy with a change of variables and achieve state-of-the-art results on spectral coarsening. Our solver further enables novel applications including volume-to-surface approximation and detaching the operator from the mesh, i.e., one can produce a mesh tailormade for visualization and optimize an operator separately for computation.