In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generative models with high fidelity, motivating the need for large training datasets. In contrast, metric preservation provides a rigorous way to control the amount of geometric distortion incurring in the construction of the latent space, leading in turn to synthetic samples of higher quality. We further demonstrate, for the first time, the adoption of differentiable intrinsic distances in the backpropagation of a geodesic loss. Our geometric priors are particularly relevant in the presence of scarce training data, where learning any meaningful latent structure can be especially challenging. The effectiveness and potential of our generative model is showcased in applications of style transfer, content generation, and shape completion.

中文翻译：

---

LIMP：使用度量保留先验学习潜在形状表示

在本文中，我们提倡采用度量保留作为学习可变形 3D 形状的潜在表示的强大先验。我们构建的关键是引入几何失真标准，直接定义在解码的形状上，将解码时度量的保留转换为底层潜在空间中线性路径的形成。我们的基本原理在于观察到单独的训练样本通常不足以赋予生成模型高保真度，从而激发对大型训练数据集的需求。相比之下，度量保留提供了一种严格的方法来控制潜在空间构造中产生的几何失真量，从而产生更高质量的合成样本。我们进一步证明，第一次，在测地线损失的反向传播中采用可微的内在距离。我们的几何先验在训练数据稀缺的情况下尤其重要，在这种情况下，学习任何有意义的潜在结构都特别具有挑战性。我们的生成模型的有效性和潜力在样式转移、内容生成和形状完成的应用中得到了展示。