Fig. 6.

An embedding of a patch P_k in its local coordinate system (frame) after it was appropriately reflected and rotated. In the noise-free case, the coordinates $p_i^{(k)}={(x_i^{(k)},y_i^{(k)},z_i^{(k)})}^{\top }$ agree with the global positioning p_i =(x_i, y_i, z_i) ^⊤ up to some translation t^(k) (unique to all i in V_k).