Progressive Decomposition of Point Clouds Without Local Planes

We present a reordering-based procedure for the multiresolution decomposition of a point cloud in this paper. The points are first reordered recursively based on an optimal pairing. Each level of reordering induces a division of the points into approximation and detail values. A balanced quantization at each level results in further compression. The original point cloud can be reconstructed without loss from the decomposition. Our scheme does not require local reference planes for encoding or decoding and is progressive. The points also lie on the original manifold at all levels of decomposition. The scheme can be used to generate different discrete LODs of the point set with fewer points in each at low BPP numbers. We also present a scheme for the progressive representation of the point set by adding the detail values selectively. This results in the progressive approximation of the original shape with dense points even at low BPP numbers. The shape gets refined as more details are added and can reproduce the original point set. This scheme uses a wavelet decomposition of the detail coefficients of the multiresolution decomposition. Progressiveness is achieved by including different levels of the DWT decomposition at all multiresolution representation levels. We show that this scheme can generate much better approximations at equivalent BPP numbers for the point set.