Quadratic Terms Based Point-to-Surface 3D Representation for Deep Learning of Point Cloud

Abstract

In this paper, we introduce a novel point-to-surface representation for 3D point cloud learning. Unlike the previous methods that mainly adopt voxel, mesh, or point coordinates, we propose to tackle this problem from a new perspective: learn a set of quadratic terms based static and global reference surfaces to describe 3D shapes, such that the coordinates of a 3D point (x, y, z) can be extended to quadratic terms (xy, xz, yz, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ldots $ </tex-math></inline-formula> ) and transformed to the relationship between the local point and the global reference surfaces. Then, the static surfaces are changed into dynamic surfaces by adaptive contribution weighting to improve the descriptive capability. Towards this end, we propose our point-to-surface representation, a new representation for 3D point cloud learning that has not been attempted before, which can assemble local and global geometric information effectively by building connections between the point cloud and the learned reference surfaces. Given 3D points, we show how the reference surfaces are constructed, and how they are inserted into the 3D learning pipeline for different tasks. The experimental results confirm the effectiveness of our new representation, which has outperformed the state-of-the-art methods on the tasks of 3D classification and segmentation.