GeoLatent: A Geometric Approach to Latent Space Design for Deformable Shape Generators
GeoLatent: A Geometric Approach to Latent Space Design for Deformable Shape Generators
复制标题
DOI：
10.1145/3618371
复制
发表时间：
2023-12
期刊：
影响因子：
--
通讯作者：
Haitao Yang;Bo Sun;Liyan Chen;Amy Pavel;Qixing Huang
中科院分区：
文献类型：
--
作者：
Haitao Yang;Bo Sun;Liyan Chen;Amy Pavel;Qixing Huang
我们研究了如何优化神经形状生成器的潜在空间，将潜在代码映射到3D可变形形状。重点是从微分几何的角度来看待可变形形状生成器。我们定义了一个黎曼度量的基础上尽可能刚性和共形变形能量。在此度量下，我们研究了潜在空间的两个期望的性质：1）潜在代码中的直线插值遵循测地线曲线; 2）潜在代码在不同尺度下解开姿势和形状变化。然而，严格执行几何插值属性仅适用于度量矩阵为常数的情况。我们展示了如何通过强制测地线插值是轴对齐的，即，沿沿着坐标轴插值遵循测地线曲线。此外，我们引入了一种新的方法，通过广义特征分解的姿态和形状的变化。我们还研究了用于学习可变形形状生成器的有效正则化项，例如，促进平滑插值。基准数据集上的实验结果表明，我们的方法导致可解释的潜在代码，提高了合成形状的泛化能力，并提高了测地线插值和测地线拍摄的性能。
We study how to optimize the latent space of neural shape generators that map latent codes to 3D deformable shapes. The key focus is to look at a deformable shape generator from a differential geometry perspective. We define a Riemannian metric based on as-rigid-as-possible and as-conformal-as-possible deformation energies. Under this metric, we study two desired properties of the latent space: 1) straight-line interpolations in latent codes follow geodesic curves; 2) latent codes disentangle pose and shape variations at different scales. Strictly enforcing the geometric interpolation property, however, only applies if the metric matrix is a constant. We show how to achieve this property approximately by enforcing that geodesic interpolations are axis-aligned, i.e., interpolations along coordinate axis follow geodesic curves. In addition, we introduce a novel approach that decouples pose and shape variations via generalized eigendecomposition. We also study efficient regularization terms for learning deformable shape generators, e.g., that promote smooth interpolations. Experimental results on benchmark datasets show that our approach leads to interpretable latent codes, improves the generalizability of synthetic shapes, and enhances performance in geodesic interpolation and geodesic shooting.