Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 Proceedings of the Symposium on Geometry Processing
Shape Recognition with Spectral Distances
IEEE Transactions on Pattern Analysis and Machine Intelligence
SHREC'10 track: feature detection and description
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
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In classical signal processing, it is common to analyze and process signals in the frequency domain, by representing the signal in the Fourier basis, and filtering it by applying a transfer function on the Fourier coefficients. In some applications, it is possible to design an optimal filter. A classical example is the Wiener filter that achieves a minimum mean squared error estimate for signal denoising. Here, we adopt similar concepts to construct optimal diffusion geometric shape descriptors. The analogy of Fourier basis are the eigenfunctions of the Laplace-Beltrami operator, in which many geometric constructions such as diffusion metrics, can be represented. By designing a filter of the Laplace-Beltrami eigenvalues, it is theoretically possible to achieve invariance to different shape transformations, like scaling. Given a set of shape classes with different transformations, we learn the optimal filter by minimizing the ratio between knowingly similar and knowingly dissimilar diffusion distances it induces. The output of the proposed framework is a filter that is optimally tuned to handle transformations that characterize the training set.