The rapid advancement of modern information technology has led to the increasing maturation of three-dimensional (3D) shape measurement technologies. At present, this technology has been applied to biomedicine, cultural relic protection, man-machine interaction, and so on. Structured light measurement emerges as a prominent 3D measurement technology, distinguished by its non-contact, high precision, and rapid speed. It stands as one of the most extensively utilized and reliable 3D measurement technologies. The de Bruijn sequence, noted for the uniqueness of any fixed length subsequence within the entire sequence, is widely employed in structured light coding. In discrete sequence coding, only one projection pattern coded by a de Bruijn sequence is required to measure the 3D information of an object, ensuring high measurement efficiency. In continuous phase-shifting coding, the de Bruijn sequence is applied to code the phase order to assist in the phase unwrapping process. However, the presence of identical consecutive codes in a de Bruijn sequence makes it challenging to precisely determine fringe numbers and positions within uniform color areas in captured images. In this paper, to solve this problem, a new type of de Bruijn sequence named adjacency-hopping de Bruijn sequence is proposed. Such sequences guarantee that all neighboring codes are different while holding the uniqueness of the subsequences. These two properties lay the foundation for accurate decoding and efficient matching. Meanwhile, an efficient and complete structured light coding and decoding process is devised by combining the adjacency-hopping de Bruijn sequence with the phase-shifting method to complete the 3D measurement task.

According to graph theory, generating a de Bruijn sequence can be accomplished by systematically traversing an Eulerian tour on a de Bruijn graph. In this paper, we redefine the vertex and edge sets of the de Bruijn graph to construct a specialized oriented graph. This oriented graph ensures that adjacent codes of each vertex are different. As a result, a unique type of de Bruijn sequence called an adjacency-hopping sequence, where all neighboring codes are guaranteed to be different, can be generated by traversing an Eulerian tour on the oriented graph. This specialized sequence is then employed to encode phase orders of the phase-shifting fringes. Specifically, the phase-shifting images are embedded into the red channel, while the phase order-encoded images via the proposed adjacency-hopping sequence are embedded into the green and blue channels. In the decoding process, color images captured by the camera are separated to calculate the wrapping phase and decode the phase order respectively. Subsequently, the Hash lookup algorithm is utilized for sequence matching, facilitating the determination of the phase order. Ultimately, 3D information is achieved.

Initially, a comparative experiment is devised to compare classic de Bruijn sequence-based coding approaches (e.g. the original de Bruijn sequence, the multi-slit de Bruijn sequence, and the recursive binary XOR sequence) with the proposed adjacency-hopping de Bruijn sequence coding method, showcasing the advantages of the proposed sequence in discrete coding. The experimental results illustrate that similar to the improved de Bruijn sequence-based approaches (i.e., the multi-slit de Bruijn sequence and the recursive binary XOR sequence), the proposed method effectively addresses the fringe separation problem encountered in the original de Bruijn sequence. Furthermore, compared with the aforementioned improved methods, the proposed adjacency-hopping de Bruijn sequence coding method demonstrates higher matching efficiency and is more suitable for integration with phase-shifting measurements. Subsequently, a series of practical measurement experiments are designed to further illustrate the processing flow of the proposed method and evaluate its performances, such as stability, measurement efficiency, and accuracy. The experimental results demonstrate that the coding and decoding method presented in this paper exhibits good robustness in scenarios involving optical path occlusions. Hence, it can be applied to measure objects with complex surface structures. Moreover, the proposed coding and decoding method achieves measurement accuracy comparable to the selected comparative phase-shifting approaches while significantly reducing the number of projected patterns, resulting in improved measurement efficiency.

We introduce a special de Bruijn sequence named the adjacency-hopping de Bruijn sequence. We theoretically prove the existence of such sequences and elucidate their generation method. The proposed sequence guarantees that all neighboring codes are different while preserving the uniqueness of subsequences. Then, the proposed sequence is employed to encode phase orders, and a novel phase-shifting-based coding method is finally introduced. On the projection side, the proposed method leads to a significant reduction in the number of projected patterns, thereby improving the projection efficiency. On the decoding side, each phase order-coded fringe can be separated accurately while guaranteeing efficient matching. The experimental results demonstrate that compared with the classical complementary Gray-code plus phase-shifting method and the multi-frequency heterodyne method, the proposed method achieves comparable measurement accuracy while reducing the number of projection patterns from 11 or 12 to 4.