Instant recovery of shape from spectrum via latent space connections
This addresses a fundamental problem in 3D vision and geometry processing for researchers and practitioners, offering a unified framework for various tasks, though it is incremental as it builds on prior methods by replacing regularizers with a learning approach.
The paper tackles the problem of recovering shapes from Laplacian spectra by introducing the first learning-based method, which replaces ad-hoc regularizers and provides more accurate results at a fraction of the computational cost, applying across dimensions, representations, and shape classes without modifications.
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.