We introduce the first learning-based method for recovering shapes from Laplacian spectra. Our model consists of a cycle-consistent module that maps between learned latent vectors of an auto-encoder and sequences of eigenvalues. This module provides an efficient and effective linkage between Laplacian spectrum and geometry. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Our learning model applies without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh superresolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and pointtopoint matching.

Marin, R., Rampini, A., Castellani, U., Rodolà, E., Ovsjanikov, M., Melzi, S. (2020). Instant recovery of shape from spectrum via latent space connections. In Proceedings. 2020 International Conference on 3D Vision. 3DV 2020 (pp.120-129). Institute of Electrical and Electronics Engineers Inc. [10.1109/3DV50981.2020.00022].

Instant recovery of shape from spectrum via latent space connections

Melzi, S
2020

Abstract

We introduce the first learning-based method for recovering shapes from Laplacian spectra. Our model consists of a cycle-consistent module that maps between learned latent vectors of an auto-encoder and sequences of eigenvalues. This module provides an efficient and effective linkage between Laplacian spectrum and geometry. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Our learning model applies without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh superresolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and pointtopoint matching.
paper
Eigenvalues and eigenfunctions; Three-dimensional displays; Finite element analysis
English
International Conference on 3D Vision (3DV)
2020
Proceedings. 2020 International Conference on 3D Vision. 3DV 2020
978-172818128-8
2020
120
129
9320393
reserved
Marin, R., Rampini, A., Castellani, U., Rodolà, E., Ovsjanikov, M., Melzi, S. (2020). Instant recovery of shape from spectrum via latent space connections. In Proceedings. 2020 International Conference on 3D Vision. 3DV 2020 (pp.120-129). Institute of Electrical and Electronics Engineers Inc. [10.1109/3DV50981.2020.00022].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/350554
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