A Volumetric Approach to Point Cloud Compression—Part I: Attribute 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 that 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. Geometry compression is addressed in Part II of this paper, while attribute compression is addressed in Part I. Attributes are represented by a volumetric function whose coefficients can be regarded as a critically sampled orthonormal transform that generalizes the recent successful Region-Adaptive Hierarchical (or Haar) Transform to higher orders. Experimental results show that attribute compression using higher order volumetric functions is an improvement over the first-order functions used in the emerging MPEG point cloud compression standard.

I. Introduction

A point cloud is a set of points (also known as locations or positions) in Euclidean space, in which a vector of attributes (such as a color triple) may be associated with each point. Point clouds may be static or dynamic. A dynamic point cloud is a sequence of static point clouds, each in its own frame. Fig. 1 shows several examples of point clouds. Point clouds have applications in robotics, tele-operation, virtual and augmented reality, cultural heritage preservation, geographic information systems, and so forth. Fig. 1.

Examples of point clouds: facades, cultural artifacts, buildings, cities, and people.