Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression

We study 3D point cloud attribute compression via a volumetric approach: assuming point cloud geometry is known at both encoder and decoder, parameters θ of a continuous attribute function f: ℝ3 mapsto ℝ are quantized to hatθ and encoded, so that discrete samples f_hatθ(xi) can be recovered at known 3D points xi ∈ ℝ3 at the decoder. Specifically, we consider a nested sequences of function subspaces F(p)l0 subseteq cdots subseteq F(p)L, where Fl(p) is a family of functions spanned by B-spline basis functions of order p, fl^* is the projection of f on Fl(p) represented as low-pass coefficients Fl^*, and gl^* is the residual function in an orthogonal subspace Gl(p) (where Gl(p) oplus Fl(p) = Fl+1(p)) represented as high-pass coefficients Gl^*. In this paper, to improve coding performance over citedo2023volumetric, we study predicting fl+1^* at level l+1 given fl^* at level l and encoding of Gl^* for the p=1 case (RAHT(1)). For the prediction, we formalize RAHT(1) linear prediction in MPEG-PCC in a theoretical framework, and propose a new nonlinear predictor using a polynomial of bilateral filter. We derive equations to efficiently compute the critically sampled high-pass coefficients Gl^* amenable to encoding. We optimize parameters in our resulting feed-forward network on a large training set of point clouds by minimizing a rate-distortion Lagrangian. Experimental results show that our improved framework outperforms the MPEG G-PCC predictor by 11%--12% in bit rate.