Marin Riccardo, Rampini Arianna, Castellani Umberto, Rodolà Emanuele, Ovsjanikov Maks, Melzi Simone
Sapienza University of Rome, Rome, Italy.
University of Verona, Verona, Italy.
Int J Comput Vis. 2021;129(10):2745-2760. doi: 10.1007/s11263-021-01492-6. Epub 2021 Jul 22.
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.
The online version supplementary material available at 10.1007/s11263-021-01492-6.
我们引入了一种基于学习的新方法，通过在学习到的潜在空间中建立和探索联系，从拉普拉斯谱中恢复形状。我们方法的核心在于一个循环一致模块，该模块在学习到的潜在空间和特征值序列之间进行映射。这个模块在编码于潜在向量中的形状几何结构与其拉普拉斯谱之间提供了一个高效且有效的联系。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，同时以一小部分计算成本提供了更准确的结果。此外，这些潜在空间联系为分析和控制可变形形状的谱特性带来了新的应用，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（二维和三维形状均适用）、表示形式（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），以及不同的形状类别，并且允许输入谱具有任意分辨率而不影响复杂度。增加的灵活性使我们能够在一个统一的框架内解决三维视觉和几何处理中众所周知的难题，包括从谱生成形状、潜在空间探索与分析、网格超分辨率、形状探索、风格迁移、点云的谱估计、分割迁移和非刚性形状匹配。
在线版本的补充材料可在10.1007/s11263-021-01492-6获取。
