PARALLEL PROCESSING OF BIG POINT CLOUDS USING Z-ORDER-BASED PARTITIONING

Abstract. As laser scanning technology improves and costs are coming down, the amount of point cloud data being generated can be prohibitively difficult and expensive to process on a single machine. This data explosion is not only limited to point cloud data. Voluminous amounts of high-dimensionality and quickly accumulating data, collectively known as Big Data, such as those generated by social media, Internet of Things devices and commercial transactions, are becoming more prevalent as well. New computing paradigms and frameworks are being developed to efficiently handle the processing of Big Data, many of which utilize a compute cluster composed of several commodity grade machines to process chunks of data in parallel.

A central concept in many of these frameworks is data locality. By its nature, Big Data is large enough that the entire dataset would not fit on the memory and hard drives of a single node hence replicating the entire dataset to each worker node is impractical. The data must then be partitioned across worker nodes in a manner that minimises data transfer across the network. This is a challenge for point cloud data because there exist different ways to partition data and they may require data transfer.

We propose a partitioning based on Z-order which is a form of locality-sensitive hashing. The Z-order or Morton code is computed by dividing each dimension to form a grid then interleaving the binary representation of each dimension. For example, the Z-order code for the grid square with coordinates (x = 1 = 01₂, y = 3 = 11₂) is 1011₂ = 11. The number of points in each partition is controlled by the number of bits per dimension: the more bits, the fewer the points. The number of bits per dimension also controls the level of detail with more bits yielding finer partitioning. We present this partitioning method by implementing it on Apache Spark and investigating how different parameters affect the accuracy and running time of the k nearest neighbour algorithm for a hemispherical and a triangular wave point cloud.