Using neighbouring nodes for the compression of octrees representing the geometry of point clouds.

The geometry of a point cloud is commonly represented by an octree recursively decomposing a 3D volume into eight child sub-volumes. Said volumes and sub-volumes are associated with nodes and child-nodes of the octree. The geometry is defined by the occupancy information indicating the presence or not of a point in each of the sub-volumes. This naturally leads to an eight-bit occupancy information to be coded for each internal node of the tree. This paper introduces a new binarization scheme to efficiently compress the occupancy information using an optimal set of binary entropy coders. Then, it is shown how using the occupancy information of neighbouring nodes helps to compress the occupancy bits associated with the child nodes of the current node. This information is used to contextualise the binarization scheme by computing, firstly a neighbour configuration, secondly a number of neighbours with occupied child nodes adjacent to the current child node, and thirdly an intra predictor. Objective results show lossless geometry compression gains between 60% and 75% on virtual reality oriented dense point clouds used by MPEG, reaching sub-bit per point bit-rates for the lossless intra coding of such point clouds. Solid gains (between 5% and 25% depending upon the sampling) are also observed on sparse point clouds captured by a LiDAR (Light Detection and Ranging) device attached to a moving vehicle or representing 3D maps.