[[File:Illustration of 3D-GCN's receptive field and kernel.png|thumb|390x390px|Illustration of 3D-GCN's receptive field and kernel]]
Graphs are constructed by kNN. 3D-GCN designs deformable 3D kernels as each kernel has one center kernel point <math>k_C\in \mathbb{R}^3</math> and several support points <math>k_1, k_2, ... k_S\in \mathbb{R}^3</math>. Given a data point <math>p_n\in \mathbb{R}^3</math>and its neighbor points <math>p_1, p_2, ... p_mp_M \in \mathbb{R}^3</math>, the convolution is operated by taking the direction vector of the center point to each neighbor <math>p_m - p_n</math> and the direction vector of the center kernel point to each support <math>k_Sk_s - k_C = k_s</math>(since <math>k_C</math> is set to be <math>(0,0,0)</math>), calculate their [[cosine similarity]], and then map this similarity to feature space by another learnable parameters <math>\mathcal{w}</math>. Since the convolution is calculated by cosine similarity instead of exact coordinate, 3D-GCN better captures an 3D object's geometry instead of ___location, and is totally '''shift and scale invariant.''' Similar to KC-Net, 3D-GCN also design a graph max-pooling to explore multi-resolution information, while preserving the largest activation.
