让点云网络精确具备平移旋转对称性，提升小数据和乱序测试下的性能
FA-KPConv: Introducing Euclidean Symmetries to KPConv via Frame Averaging
- 通过帧平均法改造KPConv，实现输入点云的精确对称性不变/等变
- 在少量训练数据和随机旋转测试下，分类与配准精度显著提升
- 不增加参数量，不丢失信息，可无缝嵌入现有KPConv模型
我们提出帧平均核点卷积（FA-KPConv），基于广泛使用的KPConv架构构建3D点云分析神经网络。尽管许多任务需要对欧几里得变换保持不变或等变性，但基于KPConv的网络仅在大规模数据集或强数据增强下近似实现该性质。通过帧平均法，我们可灵活定制基于KPConv的点云网络，使其精确具备平移、旋转和/或反射的不变性和/或等变性。只需封装现有KPConv网络，FA-KPConv即可嵌入几何先验知识，同时保持可学习参数数量不变，不损失输入信息。我们在点云分类与点云配准任务中验证了该方法的优势，尤其在训练数据稀缺或测试数据随机旋转等挑战场景下表现突出。
原文摘要 · Abstract (English)
We present Frame-Averaging Kernel-Point Convolution (FA-KPConv), a neural network architecture built on top of the well-known KPConv, a widely adopted backbone for 3D point cloud analysis. Even though invariance and/or equivariance to Euclidean transformations are required for many common tasks, KPConv-based networks can only approximately achieve such properties when training on large datasets or with significant data augmentations. Using Frame Averaging, we allow to flexibly customize point cloud neural networks built with KPConv layers, by making them exactly invariant and/or equivariant to translations, rotations and/or reflections of the input point clouds. By simply wrapping around an existing KPConv-based network, FA-KPConv embeds geometrical prior knowledge into it while preserving the number of learnable parameters and not compromising any input information. We showcase the benefit of such an introduced bias for point cloud classification and point cloud registration, especially in challenging cases such as scarce training data or randomly rotated test data.
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