High-speed three-dimensional shape measurement using geometry-constraint-based number-theoretical phase unwrapping

In this paper, we propose a high-speed three-dimensional (3-D) shape measurement technique for dynamic scenes using geometry-constraint-based number-theoretical phase unwrapping. As a classical algorithm for temporal phase unwrapping (TPU), the number-theoretical approach is suitable for the binary defocusing fringe projection system since it can retrieve an absolute phase without using low-frequency fringe patterns. However, the conventional number-theoretical TPU approach cannot provide sufficient stability to unwrap a high-frequency phase since it requires the two fringe frequencies to be coprime within the global range of the projector coordinate. In contrast, using low-frequency fringe patterns tends to make phase unwrapping more reliable, but at the expense of the measurement precision. By introducing depth constraint into the traditional number-theoretical TPU, we only need to eliminate the phase ambiguity of each pixel within a small period range defined by the depth range, which means that our method just requires the two fringe frequencies to be coprime within the local period range instead of the conventional global range. Due to the reduction of fringe order candidates and the unambiguous phase range, the reliability of phase unwrapping can be significantly improved compared with the traditional number-theoretical TPU approach even when high-frequency fringe patterns are used. The proposed method has been successfully implemented on a high-frame-rate fringe projection system, achieving high-precision, robust, and absolute 3-D shape measurement at 3333 frames per second.