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.

本文提出度量保持作为学习变形三维形状隐式表示的有力先验。其关键在于引入几何畸变准则，在解码形状上直接定义，将解码上的度量保持转化为潜在空间下的线性路径形成。度量保存提供了一种严格控制几何畸变量、从而获得更高质量的合成样本的方法，而我们的构建的有效性和潜力显示在样式迁移、内容生成和形状完整性方面。

通过度量保存先验学习隐含的形状表示

LIMP: Learning Latent Shape Representations with Metric Preservation  Priors

We introduce the first completely unsupervised correspondence learning
approach for deformable 3D shapes. Key to our model is the understanding that
natural deformations (such as changes in pose) approximately preserve the
metric structure of the surface, yielding a natural criterion to drive the
learning process toward distortion-minimizing predictions. On this basis, we
overcome the need for annotated data and replace it by a purely geometric
criterion. The resulting learning model is class-agnostic, and is able to
leverage any type of deformable geometric data for the training phase. In
contrast to existing supervised approaches which specialize on the class seen
at training time, we demonstrate stronger generalization as well as
applicability to a variety of challenging settings. We showcase our method on a
wide selection of correspondence benchmarks, where we outperform other methods
in terms of accuracy, generalization, and efficiency.

介绍了第一种完全无监督的对变形三维图形进行对应学习的方法，通过理解自然变形的形态变化近似保持曲面的度量结构，提出了一种驱动学习过程的自然准则，从而克服了对带注释数据的需求，并取而代之的是一种纯几何标准，学习模型不分含义类别，能够利用任何类型的可变形几何数据进行训练，相对于现有的专门针对训练期间观察到的类别的监督方法，我们展示出更强的泛化能力和应用于各种具有挑战性设置的能力，在广泛的对应基准测试中展示了我们的方法，在精度、泛化能力和效率方面均超过了其他方法。