🤖 AI Summary
Multi-shape Laplacian eigenbases are inherently incompatible due to spectral misalignment across non-isometric shapes, hindering consistent cross-shape functional representation and transfer.
Method: This paper proposes a correspondence-guided coupled quasi-harmonic basis construction method. By approximately jointly diagonalizing Laplacian operators and incorporating geometrically consistent correspondence priors—such as stable region indicator functions—it constructs shape-shared, frequency-aligned quasi-harmonic bases.
Contribution/Results: The method overcomes the limitation of conventional per-shape independent spectral bases and establishes, for the first time, a geometrically consistent multi-shape frequency-domain representation. It significantly improves accuracy and consistency in cross-shape function transfer across applications including shape editing, pose transfer, non-rigid matching, and shape similarity assessment. The framework provides a scalable theoretical foundation and practical toolset for multi-shape spectral analysis and collaborative processing.
📝 Abstract
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, taking as input a set of corresponding functions (e.g. indicator functions of stable regions) on the two shapes. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity.