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We introduce the first learning-based method for recovering shapes fromLaplacian spectra. Given an auto-encoder, our model takes the form of acycle-consistent module to map latent vectors to sequences of eigenvalues. Thismodule provides an efficient and effective linkage between spectrum andgeometry of a given shape. Our data-driven approach replaces the need forad-hoc regularizers required by prior methods, while providing more accurateresults at a fraction of the computational cost. Our learning model applieswithout modifications across different dimensions (2D and 3D shapes alike),representations (meshes, contours and point clouds), as well as acrossdifferent shape classes, and admits arbitrary resolution of the input spectrumwithout affecting complexity. The increased flexibility allows us to provide aproxy to differentiable eigendecomposition and to address notoriously difficulttasks in 3D vision and geometry processing within a unified framework,including shape generation from spectrum, mesh super-resolution, shapeexploration, style transfer, spectrum estimation from point clouds,segmentation transfer and point-to-point matching.

Instant recovery of shape from spectrum via latent space connections