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 https://github.com/TejasAnvekar/GPr-Net.

翻译：在三维计算机视觉应用领域，点云小样本学习发挥着关键作用。然而，由于数据具有稀疏性、不规则性和无序性，该任务面临严峻挑战。现有方法依赖卷积、图网络和注意力机制等复杂的局部几何提取技术，并需借助大规模数据驱动的预训练任务。这些方法与通过促进高效学习来实现小样本学习的根本目标相矛盾。为解决该问题，我们提出GPr-Net（几何原型网络），一种轻量级且计算高效的几何原型网络，能够捕获点云的内在拓扑结构并实现卓越性能。所提出的方法IGI++（内在几何解释器++）采用基于向量的手工设计内在几何解释器与拉普拉斯向量，用于提取和评估点云形态，从而改进小样本学习（FSL）的表征。此外，拉普拉斯向量可从点数较少的点云中提取有效特征。为应对小样本度量学习中的分布漂移挑战，我们利用双曲空间，并证明所提方法在类内与类间方差处理方面优于现有点云小样本学习方法。在ModelNet40数据集上的实验结果表明，GPr-Net在点云小样本学习任务中优于现有最优方法，其计算效率达到所有现有方法的170倍。代码已开源至https://github.com/TejasAnvekar/GPr-Net。