Suppressing motion-induced phase error by using equal-step phase-shifting algorithms in fringe projection profilometry.

Phase-shifting fringe projection profilometry is a widely used and important technique for three-dimensional surface measurement, where N-step fixed-step phase-shifting algorithms are commonly used. With a pressing need to apply this technique for dynamic object/scene measurement, the motion-induced error poses a challenge in achieving high measurement accuracy. A few correction methods have been developed by involving physical markers or complicated algorithms. In this paper, the equal-step phase-shifting algorithms are proposed as a simpler yet more effective solution. By approximating the phase variations as unknown but linear phase shifts, the equal-step algorithms are naturally immune to object motion. In particular, two classical algorithms, including the four-step Carré algorithm and the five-step Stoilov algorithm, are adopted. Furthermore, a novel three-step gradient-based equal-step phase-shifting (GEPS) algorithm is proposed. These equal-step algorithms are studied through comprehensive simulations and experiments, showing that, (i) the equal-step algorithms are all effective in greatly suppressing the motion-induced errors in both ideal and noisy situations; and (ii) among the three algorithms, the Stoilov algorithm is more robust to handle the object motion and the harmonics simultaneously, while the GEPS requires a least number of frames. This study will urge the use of the equal-step algorithms for phase extraction in dynamic profilometry for immediate motion-error suppression by merely implementing a single phase-calculation equation.

Fringe-width encoded patterns for 3D surface profilometry.

This paper presents a new fringe projection method for surface-shape measurement that uses novel fringe-width encoded fringe patterns. Specifically, the projection patterns are adjusted with the width of the fringe as the codeword. The wrapped phase with coding information is obtained by using the conventional wrapped phase calculation method, and the fringe order can be identified from the wrapped phase. After the fringe order is corrected based on the region growing algorithm, the fringe order and the wrapped phase can be directly used to reconstruct the surface. Static and dynamic measurements demonstrated the ability of the method to perform 3D shape measurement with only three projected patterns, single camera and projector in the least case.

High-resolution few-pattern method for 3D optical measurement.

Accurately and quickly obtaining the three-dimensional (3D) shape information of objects has become increasingly important in various scientific fields. However, simultaneously achieving the high-resolution and high-speed 3D shape measurement of unknown objects remains challenging in practice. In this Letter, we propose a novel variant shifting-phase method for 3D optical measurement. Based on a digital fringe projection system, the method performs a point-wise high-resolution measurement of objects by projecting only four intensity-coded patterns. We can retrieve the wrapped phases and their corresponding fringe orders simultaneously from these four patterns, and do not require any pre-acquired information of the object. The experimental results successfully demonstrate the effectiveness of the easy-to-operate method.

Fixed window aggregation AD-census algorithm for phase-based stereo matching.

Phase-based stereo matching (PSM) is a vital step in binocular structured light. PSM is hard to strike a balance between efficiency and accuracy, especially because of the absolute phase matrix's (APM) double data type. It means that PSM needs more run time and memory than conventional intensity images' stereo matching. In this paper, we propose a modified absolute difference (AD)-Census algorithm called the fixed window aggregation AD-Census (FWA-AD-Census) to balance the contradiction between efficiency and accuracy in PSM. The FWA-AD-Census aggregates matching cost in a fixed support window instead of an adaptive support window in AD-Census. We analyze the reason why PSM is more suitable to aggregate the matching cost in a fixed support window. Simulations and experiments are conducted to verify the FWA-AD-Census's performances by comparing the FWA-AD-Census with two other local stereo matching algorithms. One is the AD-Census, which is more accurate but less efficient. Its matching cost is aggregated in an adaptive support window. Another is the sum of absolute difference (SAD), which is more efficient but less accurate, and its matching cost is aggregated in a fixed support window. Theoretical analysis and experimental results both indicate that the proposed algorithm can achieve similar accuracy to the AD-Census with less run time.