提出新型点云网络,实现旋转不变下的方向感知与多尺度结构建模。
Hierarchical Direction Perception via Atomic Dot-Product Operators for Rotation-Invariant Point Clouds Learning
- 设计原子点积算子,同时实现方向选择性与旋转不变性。
- 局部用可学习点积捕捉非均匀结构,全局通过球面傅里叶变换建模方向谱。
- 在噪声和大角度旋转下表现最优,适合高鲁棒性3D视觉任务。
点云处理已成为众多3D视觉任务的核心技术。然而,任意旋转会引入点云朝向变化,长期困扰有效表征学习。根本问题在于旋转扰动破坏了点云的内在方向特性。现有方法尝试隐式建模旋转等变性与不变性,保留方向信息并传递至深层语义空间,但往往未能充分挖掘点云的多尺度方向特性以提升特征表示。为此,我们提出方向感知向量网络(DiPVNet)。其核心为原子点积算子,同时编码方向选择性与旋转不变性,赋予网络旋转对称建模与自适应方向感知能力。局部层面引入可学习局部点积(L2DP)算子,使中心点与邻点交互能自适应捕获点云的非均匀局部结构。全局层面,利用广义谐波分析证明点云与球面采样向量的点积等价于方向感知球面傅里叶变换(DASFT),由此构建全局方向响应谱以建模整体方向结构。我们严格证明了两个算子的旋转不变性。在含噪声和大角度旋转的挑战性场景中,大量实验表明,DiPVNet在点云分类与分割任务上达到当前最优性能。代码已开源:https://github.com/wxszreal0/DiPVNet。
原文摘要 · Abstract (English)
Point cloud processing has become a cornerstone technology in many 3D vision tasks. However, arbitrary rotations introduce variations in point cloud orientations, posing a long-standing challenge for effective representation learning. The core of this issue is the disruption of the point cloud's intrinsic directional characteristics caused by rotational perturbations. Recent methods attempt to implicitly model rotational equivariance and invariance, preserving directional information and propagating it into deep semantic spaces. Yet, they often fall short of fully exploiting the multiscale directional nature of point clouds to enhance feature representations. To address this, we propose the Direction-Perceptive Vector Network (DiPVNet). At its core is an atomic dot-product operator that simultaneously encodes directional selectivity and rotation invariance--endowing the network with both rotational symmetry modeling and adaptive directional perception. At the local level, we introduce a Learnable Local Dot-Product (L2DP) Operator, which enables interactions between a center point and its neighbors to adaptively capture the non-uniform local structures of point clouds. At the global level, we leverage generalized harmonic analysis to prove that the dot-product between point clouds and spherical sampling vectors is equivalent to a direction-aware spherical Fourier transform (DASFT). This leads to the construction of a global directional response spectrum for modeling holistic directional structures. We rigorously prove the rotation invariance of both operators. Extensive experiments on challenging scenarios involving noise and large-angle rotations demonstrate that DiPVNet achieves state-of-the-art performance on point cloud classification and segmentation tasks. Our code is available at https://github.com/wxszreal0/DiPVNet.
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