Mapping data on a rotated grid in high-dimensions for lossless compression

Interactive navigation of large high-dimensional media datasets aims at allowing viewers to freely navigate content, selecting a subset of the high-dimensional visual data of interest for display. An example application would be remote visualization of an arbitrary 2-D planar cut from a large volumetric dataset with random access. In our previous work, we proposed a server-client based data representation and retrieval system using overlapping rotated tiles to represent the dataset, which lower the bandwidth required for accessing a random plane from large volume data. This leads to the question of how best to represent these rotated tiles for compression. In this paper we present a non-interpolated symmetric mapping algorithm, which maps each voxel in the original image to a rotated Cartesian grid point. We will show that this approach outperforms tile representation methods based on interpolation and non-symmetric mapping. In particular, the lack of interpolation means that complexity is significantly lower. Moreover, especially at high rates, remapping without interpolation will be shown to lead to overall better RD performance and the more symmetric the mapping is, the better RD performance will be achieved. Furthermore, a metric is proposed for automatically checking the mapping symmetry and measuring the percentage of the non-symmetric mapped points in the non-symmetric mapping algorithms.