A Volumetric Approach to Point Cloud Compression–Part II: Geometry Compression

Compression of point clouds has so far been confined to coding the positions of a discrete set of points in space and the attributes of those discrete points. We introduce an alternative approach based on volumetric functions, which are functions defined not just on a finite set of points, but throughout space. As in regression analysis, volumetric functions are continuous functions that are able to interpolate values on a finite set of points as linear combinations of continuous basis functions. Using a B-spline wavelet basis, we are able to code volumetric functions representing both geometry and attributes. Attribute compression is addressed in Part I of this paper, while geometry compression is addressed in Part II. Geometry is represented implicitly as the level set of a volumetric function (the signed distance function or similar). Experimental results show that geometry compression using volumetric functions improves over the methods used in the emerging MPEG Point Cloud Compression (G-PCC) standard.

I. Introduction

There are two parts to the point cloud compression problem: geometry compression and attribute compression. In Part I of this paper [1], we addressed the problem of attribute compression: how to represent and compress attributes on a given set of point locations . In that case, the point locations were assumed to be communicated out-of-band as side information and reconstructed at the decoder, either with or without loss. In the present part of the paper (Part II), we address the geometry compression problem: how to represent and compress the point locations themselves.