In the realm of 3D-computer vision applications, point cloud few-shot
learning plays a critical role. However, it poses an arduous challenge due to
the sparsity, irregularity, and unordered nature of the data. Current methods
rely on complex local geometric extraction techniques such as convolution,
graph, and attention mechanisms, along with extensive data-driven pre-training
tasks. These approaches contradict the fundamental goal of few-shot learning,
which is to facilitate efficient learning. To address this issue, we propose
GPr-Net (Geometric Prototypical Network), a lightweight and computationally
efficient geometric prototypical network that captures the intrinsic topology
of point clouds and achieves superior performance. Our proposed method, IGI++
(Intrinsic Geometry Interpreter++) employs vector-based hand-crafted intrinsic
geometry interpreters and Laplace vectors to extract and evaluate point cloud
morphology, resulting in improved representations for FSL (Few-Shot Learning).
Additionally, Laplace vectors enable the extraction of valuable features from
point clouds with fewer points. To tackle the distribution drift challenge in
few-shot metric learning, we leverage hyperbolic space and demonstrate that our
approach handles intra and inter-class variance better than existing point
cloud few-shot learning methods. Experimental results on the ModelNet40 dataset
show that GPr-Net outperforms state-of-the-art methods in few-shot learning on
point clouds, achieving utmost computational efficiency that is $170\times$
better than all existing works. The code is publicly available at
this https URL

提出了一种轻量级的计算几何原型网络 GPr-Net，结合基于向量的手工内在几何量子化器和拉普拉斯向量等相关方法，旨在解决点云匮乏和无序性等问题，并使用超几何空间来处理分布漂移问题，结果表明在计算机效率和精确度上优于所有已有的点云小样本学习方法。