1b115b1feab2198dd0881c57b869ddb7-Supplemental-Conference.pdf

In order to expand the polynomial surface fitting in 3D dimensional space into the high dimensional feature space using a neural network with parameter Θ, we define f1(gω):= g and f2(cυ):= c, where f means MLP layer. Then, the multiplication of real numbers gω cυ in the polynomial function is represented as g c, i.e., gω cυ:= g c, and the orders ω,υ [0,1,...,τ]. Then, the final bivariate function used in our hyper surface fitting is Nθ,τ(G,C) = Θ(G C), where Gand C are high dimensional features of the 3D point clouds extracted by the two different modules, which are introduced in Sec.3.3 and Sec.3.4 of the paper, respectively. The other terms except the principal terms in the polynomial equation are not used in the estimation of the normal. Based on this, we use the max-pooling over all features from the hyper surface fitting 2 Figure 1: Visualization of the contribution of each 3D point to estimate the normal of the query point (black).