ShapeFlow：三维曲面中的可学习变形
ShapeFlow: Learnable Deformations Among 3D Shapes
摘要：
我们提出了ShapeFlow，一个基于流的模型，用于学习具有较大类内变化的整个3D形状类的变形空间。ShapeFlow允许学习多模板变形空间，该空间与形状拓扑无关，但保留了精细的几何细节。与其中将潜在向量直接解码成形状的生成空间不同，变形空间将向量解码成可以将源形状向目标平流输送的连续流。这样的空间自然允许几何风格（来自源）和结构姿态（符合目标）的解开。我们参数化的几何形状之间的变形作为一个学习的连续流场通过神经网络，并表明，这种变形可以保证具有理想的属性，如双射性，自由自相交，或体积保存。我们说明了这种学习变形空间的各种下游应用程序的有效性，包括形状生成通过变形，几何风格转移，无监督学习的一致参数化的整个类的形状，形状插值。
英文摘要：
We present ShapeFlow, a flow-based model for learning a deformation space for entire classes of 3D shapes with large intra-class variations. ShapeFlow allows learning a multi-template deformation space that is agnostic to shape topology, yet preserves fine geometric details. Different from a generative space where a latent vector is directly decoded into a shape, a deformation space decodes a vector into a continuous flow that can advect a source shape towards a target. Such a space naturally allows the disentanglement of geometric style (coming from the source) and structural pose (conforming to the target). We parametrize the deformation between geometries as a learned continuous flow field via a neural network and show that such deformations can be guaranteed to have desirable properties, such as be bijectivity, freedom from self-intersections, or volume preservation. We illustrate the effectiveness of this learned deformation space for various downstream applications, including shape generation via deformation, geometric style transfer, unsupervised learning of a consistent parameterization for entire classes of shapes, and shape interpolation.
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