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.
GLYPH-SR: Can We Achieve Both High-Quality Image Super-Resolution and High-Fidelity Text Recovery via VLM-guided Latent Diffusion Model?
Department of Artificial Intelligence（人工智能系）；Kyungpook National University（庆尚国立大学）；Department of Electrical and Computer Engineering（电气电子工程系）；Queen’s University（皇后大学）；Department of Information and Communications Engineering（信息与通信工程系）；Pukyong National University（浦项国立大学）
Adaptive Structure-constrained Robust Latent Low-Rank Coding for Image Recovery
Soochow University（苏州大学）；Hefei University of Technology（合肥工业大学）；University of Georgia（佐治亚大学）；Harbin Institute of Technology (Shenzhen)（哈尔滨工业大学（深圳））；University of Science and Technology of China（中国科学技术大学）
DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery
University of Electronic Science and Technology of China（电子科技大学）；Southwest Jiaotong University（西南交通大学）；Jiangxi University of Finance and Economics（江西财经大学）；City University of Hong Kong（香港城市大学）
PointLIE: Locally Invertible Embedding for Point Cloud Sampling and Recovery
Shenzhen Research Institute of Big Data（深圳市大数据研究院）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shanghai University（上海大学）；Shenzhen Luohu Hospital（深圳市罗湖医院）
Platonic Representations in the Human Brain: Unsupervised Recovery of Universal Geometry
Department of Cognition, Development and Education Psychology, University of Barcelona（巴塞罗那大学认知、发展与教育心理学系）；Institute of Neurosciences, University of Barcelona（巴塞罗那大学神经科学研究所）；Department of Computer Science, Cornell University（康奈尔大学计算机科学系）；Bellvitge Institute for Biomedical Research, Spain（西班牙贝尔维德生物医学研究 institute）
