  The goal of objective point cloud quality assessment (PCQA) research is to
develop quantitative metrics that measure point cloud quality in a perceptually
consistent manner. Merging the research of cognitive science and intuition of
the human visual system (HVS), in this paper, we evaluate the point cloud
quality by measuring the complexity of transforming the distorted point cloud
back to its reference, which in practice can be approximated by the code length
of one point cloud when the other is given. For this purpose, we first make
space segmentation for the reference and distorted point clouds based on a 3D
Voronoi diagram to obtain a series of local patch pairs. Next, inspired by the
predictive coding theory, we utilize a space-aware vector autoregressive
(SA-VAR) model to encode the geometry and color channels of each reference
patch with and without the distorted patch, respectively. Assuming that the
residual errors follow the multi-variate Gaussian distributions, the
self-complexity of the reference and transformational complexity between the
reference and distorted samples are computed using covariance matrices.
Additionally, the prediction terms generated by SA-VAR are introduced as one
auxiliary feature to promote the final quality prediction. The effectiveness of
the proposed transformational complexity based distortion metric (TCDM) is
evaluated through extensive experiments conducted on five public point cloud
quality assessment databases. The results demonstrate that TCDM achieves
state-of-the-art (SOTA) performance, and further analysis confirms its
robustness in various scenarios. The code is publicly available at
https://github.com/zyj1318053/TCDM.
