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The networks for point cloud tasks are expected to be invariant when the
point clouds are affinely transformed such as rotation and reflection. So far,
relative to the rotational invariance that has been attracting major research
attention in the past years, the reflection invariance is little addressed.
Notwithstanding, reflection symmetry can find itself in very common and
important scenarios, e.g., static reflection symmetry of structured streets,
dynamic reflection symmetry from bidirectional motion of moving objects (such
as pedestrians), and left- and right-hand traffic practices in different
countries. To the best of our knowledge, unfortunately, no reflection-invariant
network has been reported in point cloud analysis till now. To fill this gap,
we propose a framework by using quadratic neurons and PCA canonical
representation, referred to as Cloud-RAIN, to endow point \underline{Cloud}
models with \underline{R}eflection\underline{A}l \underline{IN}variance. We
prove a theorem to explain why Cloud-RAIN can enjoy reflection symmetry.
Furthermore, extensive experiments also corroborate the reflection property of
the proposed Cloud-RAIN and show that Cloud-RAIN is superior to data
augmentation. Our code is available at
https://github.com/YimingCuiCuiCui/Cloud-RAIN.
