论文标题
定义由d维对象投影生成的图像的SO（D） - 转向的动作：用几何VAE构成推理的应用
Defining an action of SO(d)-rotations on images generated by projections of d-dimensional objects: Applications to pose inference with Geometric VAEs
论文作者
论文摘要
差异自动编码器（VAE）的最新进展使学习潜流歧管成为紧凑的谎言组，例如$ so（d）$。由于这种方法假定数据在于谎言组本身同构的子空间，因此我们在这里研究了该假设如何在图像的背景下通过预测$ d $尺寸的量产生的图像，而$ d $ d $（d）$。在检查了组和图像空间的不同理论候选者后，我们表明，定义对数据空间的组动作的尝试通常会失败，因为它需要对卷上的更具体的几何约束。使用几何VAE，我们的实验证实了此约束是适当姿势推断的关键，我们讨论了这些结果对应用和未来工作的潜力。
Recent advances in variational autoencoders (VAEs) have enabled learning latent manifolds as compact Lie groups, such as $SO(d)$. Since this approach assumes that data lies on a subspace that is homeomorphic to the Lie group itself, we here investigate how this assumption holds in the context of images that are generated by projecting a $d$-dimensional volume with unknown pose in $SO(d)$. Upon examining different theoretical candidates for the group and image space, we show that the attempt to define a group action on the data space generally fails, as it requires more specific geometric constraints on the volume. Using geometric VAEs, our experiments confirm that this constraint is key to proper pose inference, and we discuss the potential of these results for applications and future work.
