FIGURE 13.

Overview of the SO(3)-equivariant registration network (Zhu et al., 2022b). The point cloud input is of shape ${\mathbb{R}}^{N\times 3}$ , and the encoded feature is of shape ${\mathbb{R}}^{C\times 3}$ . N is the number of points, and C is the dimension of features. Occupancy field is a function $v(p)\mapsto [\mathrm{0,1}],p\in {\mathbb{R}}^3$ mapping any 3D coordinate to an occupancy value. The rotation is estimated by aligning the features using Horn’s method (Horn et al., 1988).