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Coupled quasi‐harmonic bases
Author(s) -
Kovnatsky A.,
Bronstein M. M.,
Bronstein A. M.,
Glashoff K.,
Kimmel R.
Publication year - 2013
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12064
Subject(s) - computer science , computer graphics , similarity (geometry) , laplace operator , set (abstract data type) , graphics , harmonic , algorithm , laplacian matrix , theoretical computer science , artificial intelligence , topology (electrical circuits) , mathematics , computer graphics (images) , image (mathematics) , mathematical analysis , combinatorics , graph , physics , quantum mechanics , programming language
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.