Coupled quasi-harmonic bases
This addresses a bottleneck in multi-shape applications in computer graphics, offering an incremental improvement over existing methods.
The paper tackled the incompatibility of independently computed Laplacian eigenbases across multiple shapes by proposing a method to construct common approximate eigenbases, demonstrating benefits in shape editing, pose transfer, correspondence, and similarity tasks.
The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity.