Divide and conquer: high-accuracy and real-time 3D reconstruction of static objects using multiple-phase-shifted structured light illumination.

Multiple-phase-shifted structured light illumination achieves high-accuracy 3D reconstructions of static objects, while typically it can't achieve real-time phase computation. In this paper, we propose to compute modulations and phases of multiple scans in real time by using divide-and-conquer solutions. First, we categorize total N = KM images into M groups and each group contains K phase equally shifted images; second, we compute the phase of each group; and finally, we obtain the final phase by averaging all the separately computed phases. When K = 3, 4 or 6, we can use integer-valued intensities of images as inputs and build one or M look-up tables storing real-valued phases computed by using arctangent function. Thus, with addition and/or subtraction operations computing indices of the tables, we can directly access the pre-computed phases and avoid time-consuming arctangent computation. Compared with K-step phase measuring profilometry repeated for M times, the proposed is robust to nonlinear distortion of structured light systems. Experiments show that, first, the proposed is of the same accuracy level as the traditional algorithm, and secondly, with employing one core of a central processing unit, compared with the classical 12-step phase measuring profilometry algorithm, for K = 4 and M = 3, the proposed improves phase computation by a factor of 6 ×.

Extending epipolar geometry for real-time structured light illumination.

Structured light illumination, scanning along both horizontal and vertical directions, achieves more robust accuracy. By introducing the constraint of epipolar geometry, we previously proposed real-time 3D reconstruction using lookup tables; however, we only knew these offline derived tables were the combinations of the elements in calibration matrices of a camera and a projector, and suffered from long-time computation. In this Letter, by parameterizing the line perspectively mapping a 3D world coordinate into the camera and projector spaces, we propose to extend the epipolar analysis by defining phase and optical poles. Thus, we can geometrically address these parameters via analytic closed-form equations, with which we can (1) directly derive lookup tables in real time from the calibration matrices and (2) optimally reduce the number of tables from 11 to 5 to save much more memory space while further accelerating the processing rate. Experiments show that with the same level of accuracy, we significantly reduce the time to compute the lookup tables from more than 20 min to 20 ms, and increase the speed of computing point clouds from approximately 320 to 492 fps.