Toward optimal structured light patterns

A methodology for the optimal design of projection patterns for stereometric structured light systems is presented. It draws on the similarity as well as the difference between the design of projection patterns and the design of optimal signals for digital communication. Seemingly unrelated structured light methods, such as the Gray code scheme and intensity ratio techniques, are unified as special cases within the suggested theoretical framework. The design of K projection patterns for a structured light system with L distinct planes of light turns out to be equivalent to the placement of L points in a K-dimensional space subject to certain constraints. Optimal design in the MSE sense can be defined, but leads to an intractable multi-parameter global optimization problem. Intuitively appealing suboptimal solutions are derived from the family of K-dimensional space-filling Hilbert curves. The theoretical results are supported by experiments.