We introduce a novel learning-based method to recover shapes from their Laplacian spectra, based on establishing and exploring connections in a learned latent space. The core of our approach consists in a cycle-consistent module that maps between a learned latent space and sequences of eigenvalues. This module provides an efficient and effective link between the shape geometry, encoded in a latent vector, and its Laplacian spectrum. Our proposed 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. Moreover, these latent space connections enable novel applications for both analyzing and controlling the spectral properties of deformable shapes, especially in the context of a shape collection. Our learning model and the associated analysis apply without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), nature of the latent space (generated by an auto-encoder or a parametric model), 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, latent space exploration and analysis, mesh super-resolution, shape exploration, style transfer, spectrum estimation for point clouds, segmentation transfer and non-rigid shape matching.

我们引入了一种新的基于学习的方法来从拉普拉斯光谱中恢复形状，基于在学习的潜在空间中建立和探索连接。我们方法的核心在于一个循环一致的模块，该模块在学习的潜在空间和特征值序列之间进行映射。该模块在以潜在向量编码的形状几何与其拉普拉斯谱之间提供了高效且有效的链接。我们提出的数据驱动方法取代了先前方法所需的临时正则化器的需求，同时以一小部分计算成本提供更准确的结果。此外，这些潜在空间连接为分析和控制可变形形状的光谱特性提供了新的应用，特别是在形状集合的背景下。我们的学习模型和相关分析无需修改即可应用于不同维度（2D 和 3D 形状等）、表示（网格、轮廓和点云）、潜在空间的性质（由自动编码器或参数模型生成），如以及跨不同的形状类别，并允许输入光谱的任意分辨率而不影响复杂性。增加的灵活性使我们能够在统一的框架内解决 3D 视觉和几何处理中众所周知的困难任务，包括从光谱生成形状、潜在空间探索和分析、网格超分辨率、形状探索、样式转移、点云的光谱估计、分割转移和非刚性形状匹配。表示（网格、轮廓和点云）、潜在空间的性质（由自动编码器或参数模型生成）以及跨不同的形状类别，并允许输入频谱的任意分辨率而不影响复杂性。增加的灵活性使我们能够在统一的框架内解决 3D 视觉和几何处理中众所周知的困难任务，包括从光谱生成形状、潜在空间探索和分析、网格超分辨率、形状探索、样式转移、点云的光谱估计、分割转移和非刚性形状匹配。表示（网格、轮廓和点云）、潜在空间的性质（由自动编码器或参数模型生成）以及跨不同的形状类别，并允许输入频谱的任意分辨率而不影响复杂性。增加的灵活性使我们能够在统一的框架内解决 3D 视觉和几何处理中众所周知的困难任务，包括从光谱生成形状、潜在空间探索和分析、网格超分辨率、形状探索、样式转移、点云的光谱估计、分割转移和非刚性形状匹配。并允许输入频谱的任意分辨率而不影响复杂性。增加的灵活性使我们能够在统一的框架内解决 3D 视觉和几何处理中众所周知的困难任务，包括从光谱生成形状、潜在空间探索和分析、网格超分辨率、形状探索、样式转移、点云的光谱估计、分割转移和非刚性形状匹配。并允许输入频谱的任意分辨率而不影响复杂性。增加的灵活性使我们能够在统一的框架内解决 3D 视觉和几何处理中众所周知的困难任务，包括从光谱生成形状、潜在空间探索和分析、网格超分辨率、形状探索、样式转移、点云的光谱估计、分割转移和非刚性形状匹配。