# Instant recovery of shape from spectrum via latent space connections

arXiv: https://arxiv.org/abs/2003.06523 · HTML: https://mlsanity.com/paper/2003.06523/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Shape registration in the time of transformers](https://mlsanity.com/paper/2106.13679/) (2021)
- [Universal Spectral Adversarial Attacks for Deformable Shapes](https://mlsanity.com/paper/2104.03356/) (2021)
- [Neural Human Deformation Transfer](https://mlsanity.com/paper/2109.01588/) (2021)
- [Latent Spectral Regularization for Continual Learning](https://mlsanity.com/paper/2301.03345/) (2023)
- [Learning Spectral Unions of Partial Deformable 3D Shapes](https://mlsanity.com/paper/2104.00514/) (2021)
- [Anytime 3D Object Reconstruction using Multi-modal Variational Autoencoder](https://mlsanity.com/paper/2101.10391/) (2021)
- [Disentangling Geometric Deformation Spaces in Generative Latent Shape Models](https://mlsanity.com/paper/2103.00142/) (2021)
- [SAGA: Spectral Adversarial Geometric Attack on 3D Meshes](https://mlsanity.com/paper/2211.13775/) (2022)
- [DifAttack++: Query-Efficient Black-Box Adversarial Attack via Hierarchical Disentangled Feature Space in Cross-Domain](https://mlsanity.com/paper/2406.03017/) (2024)
- [Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach](https://mlsanity.com/paper/2108.02161/) (2021)

## Abstract (arXiv)

We introduce the first learning-based method for recovering shapes from Laplacian spectra. Given an auto-encoder, our model takes the form of a cycle-consistent module to map latent vectors to sequences of eigenvalues. This module provides an efficient and effective linkage between spectrum and geometry of a given shape. 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 provide a proxy to differentiable eigendecomposition and to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh super-resolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and point-to-point matching.