PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNs
- URL: http://arxiv.org/abs/2208.03720v1
- Date: Sun, 7 Aug 2022 13:37:29 GMT
- Title: PDO-s3DCNNs: Partial Differential Operator Based Steerable 3D CNNs
- Authors: Zhengyang Shen, Tao Hong, Qi She, Jinwen Ma, Zhouchen Lin
- Abstract summary: In this work, we employ partial differential operators (PDOs) to model 3D filters, and derive general steerable 3D CNNs called PDO-s3DCNNs.
We prove that the equivariant filters are subject to linear constraints, which can be solved efficiently under various conditions.
- Score: 69.85869748832127
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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.
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