论文标题
PDO-S3DCNNS：基于部分差分运算符的可检测3D CNNS
PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNs
论文作者
论文摘要
可进入的模型可以通过在表示理论和特征领域的语言中制定均衡性要求来提供非常通用和灵活的均衡性，这被认为对许多视觉任务都是有效的。但是，由于3D旋转的数学更复杂，因此在2D情况下得出3D旋转模型要困难得多。在这项工作中，我们采用部分差分运算符（PDOS）来模型3D过滤器，并得出了通用的可通道的3D CNN，称为PDO-S3DCNNS。我们证明，等效过滤器受线性约束的约束，可以在各种条件下有效地解决。据我们所知，PDO-S3DCNN是最通用的3D旋转的CNN，因为它们涵盖了所有$ SO（3）$及其表示的所有常见子组，而现有方法只能应用于特定的组和表示。广泛的实验表明，我们的模型可以很好地保留在离散域中的均衡性，并且在SHEREC'17检索和ISBI 2012分割任务上的表现优于以前的网络复杂性。
Steerable models can provide very general and flexible equivariance by formulating equivariance requirements in the language of representation theory and feature fields, which has been recognized to be effective for many vision tasks. However, deriving steerable models for 3D rotations is much more difficult than that in the 2D case, due to more complicated mathematics of 3D rotations. In this work, we employ partial differential operators (PDOs) to model 3D filters, and derive general steerable 3D CNNs, which are called PDO-s3DCNNs. We prove that the equivariant filters are subject to linear constraints, which can be solved efficiently under various conditions. As far as we know, PDO-s3DCNNs are the most general steerable CNNs for 3D rotations, in the sense that they cover all common subgroups of $SO(3)$ and their representations, while existing methods can only be applied to specific groups and representations. Extensive experiments show that our models can preserve equivariance well in the discrete domain, and outperform previous works on SHREC'17 retrieval and ISBI 2012 segmentation tasks with a low network complexity.
