Taylor Series-Inspired Local Structure Fitting Network for Few-shot Point Cloud Semantic Segmentation

Few-shot point cloud semantic segmentation aims to accurately segment "unseen" new categories in point cloud scenes using limited labeled data. However, pretraining-based methods not only introduce excessive time overhead but also overlook the local structure representation among irregular point clouds. To address these issues, we propose a pretraining-free local structure fitting network for few-shot point cloud semantic segmentation, named TaylorSeg. Specifically, inspired by Taylor series, we treat the local structure representation of irregular point clouds as a polynomial fitting problem and propose a novel local structure fitting convolution, called TaylorConv. This convolution learns the low-order basic information and high-order refined information of point clouds from explicit encoding of local geometric structures. Then, using TaylorConv as the basic component, we construct two variant of TaylorSeg: a non-parametric TaylorSeg-NN and a parametric TaylorSeg-PN. The former can achieve performance comparable to existing parametric models without pretraining. For the latter, we equip it with an Adaptive Push-Pull (APP) module to mitigate the feature distribution differences between the query set and the support set. Extensive experiments validate the effectiveness of the proposed method. Notably, under the 2-way 1-shot setting, TaylorSeg-PN achieves improvements of +2.28% and +4.37% mIoU on the S3DIS and ScanNet datasets respectively, compared to the previous state-of-the-art methods.