Rethinking 3D Convolution in \ell_p -norm Space

Convolution is a fundamental operation in the 3D backbone. However, under certain conditions, the feature extraction ability of traditional convolution methods may be weakened. In this paper, we introduce a new convolution method based on $\ell_p$-norm. For theoretical support, we prove the universal approximation theorem for $\ell_p$-norm based convolution, and analyze the robustness and feasibility of $\ell_p$-norms in 3D point cloud tasks. Concretely, $\ell_{\infty}$-norm based convolution is prone to feature loss.