  Rate distortion optimization plays a very important role in image/video
coding. But for 3D point cloud, this problem has not been investigated. In this
paper, the rate and distortion characteristics of 3D point cloud are
investigated in detail, and a typical and challenging rate distortion
optimization problem is solved for 3D point cloud. Specifically, since the
quality of the reconstructed 3D point cloud depends on both the geometry and
color distortions, we first propose analytical rate and distortion models for
the geometry and color information in video-based 3D point cloud compression
platform, and then solve the joint bit allocation problem for geometry and
color based on the derived models. To maximize the reconstructed quality of 3D
point cloud, the bit allocation problem is formulated as a constrained
optimization problem and solved by an interior point method. Experimental
results show that the rate-distortion performance of the proposed solution is
close to that obtained with exhaustive search but at only 0.68% of its time
complexity. Moreover, the proposed rate and distortion models can also be used
for the other rate-distortion optimization problems (such as prediction mode
decision) and rate control technologies for 3D point cloud coding in the
future.
