Accompanying paper?
Isospectralization is a novel numerical procedure allowing to deform a shape one shape such that its spectrum matches that of another - thus hearing the shape of the drum. Isospectralizing two shapes is a simple preprocessing that dramatically improves intrinsic correspondence.pic.twitter.com/GSneKf4OXd
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Laplacian eigenvalues (spectrum) can be interpreted as natural vibration frequencies of the shape. They are known to carry information about many geometric and topological characteristics such as genus, area, total curvature etc.
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Have you tried concave polygons, like the classical counter examples of planar isospectral domains?
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Yes - the issue with such experiments is that numerically they are not exactly isospectral when triangulated. We saw convergence to one of the polygons rather than one of the two depending on the initialization.
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And implementation? This could be useful for brain research!
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