Integer Alternative for the Region-Adaptive Hierarchical Transform

A recently-introduced coder based on region-adaptive hierarchical transform (RAHT) is being considered as a standard for the compression of point cloud attributes at moving picture experts group. The RAHT coefficients can be encoded in many ways and the transform is based on a series of orthogonal 2 × 2 transform matrices with geometry-dependent floating-point entries. In order to remove computation ambiguity and facilitate deployment, fixed-point operations are often preferred. In this letter, we present an alternative RAHT description that allows for fixed-point implementation of its transform steps. It is based on matrix decompositions akin to lifting steps and a scaling of the quantization steps. Results are presented to show that the new fixed-point transform is, in practical terms, equivalent to the floating-point RAHT. For that we use a reasonable number of precision bits for the integer operations, e.g. 8 b or more.