Abstract. 3D Convolutional Neural Networks are sensitive to transformations applied to their input. This is a problem because a voxelized version of a
3D object, and its rotated clone, will look unrelated to each other after passing
through to the last layer of a network. Instead, an idealized model would
preserve a meaningful representation of the voxelized object, while explaining
the pose-difference between the two inputs. An equivariant representation
vector has two components: the invariant identity part, and a discernable
encoding of the transformation. Models that can’t explain pose-differences
risk “diluting” the representation, in pursuit of optimizing a classification or
regression loss function.
We introduce a Group Convolutional Neural Network with linear equivariance to translations and right angle rotations in three dimensions. We call
this network CubeNet, reflecting its cube-like symmetry. By construction,
this network helps preserve a 3D shape’s global and local signature, as it is
transformed through successive layers. We apply this network to a variety of
3D inference problems, achieving state-of-the-art on the ModelNet10 classification challenge, and comparable performance on the ISBI 2012 Connectome
Segmentation Benchmark. To the best of our knowledge, this is the first 3D
rotation equivariant CNN for voxel representations.