Abstract:
Shape analysis tasks, including mesh classification, segmentation, and
retrieval demonstrate symmetries in Euclidean space and should be invariant
to geometric transformations such as rotation and translation. However,
existing methods in mesh analysis often rely on extensive data augmentation
and more complex analysis models to handle 3D rotations. Despite these
efforts, rotation invariance is not guaranteed, which can significantly
reduce accuracy when test samples undergo arbitrary rotations, because the
analysis method struggles to generalize to the unknown orientations of the
test samples. To address these challenges, our work presents a novel
approach that employs graph neural networks (GNNs) to analyze
mesh-structured data. Our proposed GNN layer, aggregation function, and
local pooling layer are equivariant to the rotation, reflection and
translation of 3D shapes, making them suitable building blocks for our
proposed rotation-invariant network for the classification of mesh models.
Therefore, our proposed approach does not need rotation augmentation, and
we can maintain accuracy even when test samples undergo arbitrary rotations.
Extensive experiments on various datasets demonstrate that our methods
achieve state-of-the-art performance.
